The problem:
If vanilla V.A.T.S is turned into bullet time using the common methods; many effects, perks, hit-events, and all the good stuff will not work.  
As a result some perks are wonky, Awareness doesn't work, Gun-Fu cant trigger, Concentrated Fire is pointless.  
We can't do limb damage, critting requires workarounds, and any effect that needs to know what body part it hit simply fails.   

This mod attempts to solve that.
Your controllers VATS button will from now on start Bullet Time V.A.T.S.

Bullet Time V.A.T.S mostly works like vanilla VATS. You can use all the "when in VATS" perks, effects will fire, you do limb damage, there is damage reduction (configurable), slow-time (configurable), and if you have awareness you can identify a target's hp and resistances.

Different from vanilla VATS is that you can move around, take scoped shots, equip and use items, and throw grenades.  
Melee users can damage limbs in Bullet Time V.A.T.S, something that is not possible even in unmodded vanilla VATS.   

Overview

Possible actions:  

• Move
• Jump
• Use Scope
• Equip
• Eat, Drink, Chems
• Throw
• Use PipBoy
• Use Favorites
• Limb Damage for Melee users
• Most vanilla VATS actions
  

AP Consumption:
Most actions you can take in Bullet Time V.A.T.S will cost Action Points.  
The cost can be partially configured in the holotape.

• Scoped shot.
  Take advantage of slow time and land a sniper shot on a moving target.
  It will cost ALL off your AP and kick you out of VATS.  The Sniper 3 perk halves the AP cost, allowing 2 shots. 

• Moving and jumping.
  Moving is expensive, so is jumping. But it's cool to go Max Payne on those raiders.
  The Blitz perks will massively reduce movement costs.

• Equipping items.
  You can equip a weapon for 1/3 of your max AP.
  Equipping armor is free. If you can be the Silver Shroud you should be able to change costumes as fast as superheroes do.
  Equipping legendary armor that has an effect on AP will cost half of your max AP.

• Eating, drinking, and using Chems.
  Will cost you a third of your max AP.

• Using throwables. (grenades, mines, etc)
  Using slow time to create a hails of grenades is very overpowered, therefore a throw will cost 1/3 of your AP.

Settings Holotape:

• Time Dilation.
  Choose from  several options in a range from the vanilla 0.04 to 0.75
• Image Space Modifier.
  Select from 3 Image Space Effects, or disable them.
• Set AP consumption rate.
  The default option matches vanilla VATS. You can increase or decrease the rate.  
• V.A.T.S Defence.
  Choose how strong you want VATS damage reduction to be. Off is an option. 
• Enable or disable Awareness perk effect.  
  Dislike the workaround I made for Awareness? Then you can turn it off here. 
• Movement settings.  
  Choose from Direct Move or Teleport.
• Button Setup
  Help the script find what button your controller uses for VATS.  

Critical Hits:
For crits I worked under the assumption that everyone who wants bullet time is using "Critical Hits Outside of VATS"  
I changed critical banker to be complimentary to that mod, allowing for a Luck+crits VATS build just like in vanilla.
You don't bank crits in Bullet Time V.A.T.S, but with some effort you can achieve over 50% crit chance while in VATS.    

Perks:
In no particular order here is what changed to the perks:

- Awareness
Rank 1 identifies a targets name, level, HP, and resistances.   
When you aim at a target they are shortly highlighted and a help message appears on your HUD to displays their info. This also works in scopes.  
If you dislike this feature you can disable it in the settings holotape.
Rank 2 gives you 5% extra damage

- Mysterious Stranger.  
changed to work in Bullet Time V.A.T.S.  
The only difference is that your crit meter does not get filled, because we dont have one.

- Grim Reapers Sprint
changed to work in Bullet Time V.A.T.S exactly like it did in vanilla VATS

- Sniper 3
You can now fire two scoped shots if you have enough AP.
Scoring a scoped hit in Bullet Time V.A.T.S costs all of your AP. It's a free hit thanks to slowed time so this a fair trade. This perk allows for 2 shots in Bullet Time V.A.T.S.

- Concentrated Fire
Your guns do more Limb Damage in V.A.T.S.
Keeping track of how often an actors limb is hit is too heavy on the script engine. I chose to replace it with simple +LimbDamage.
The ranks are 30%, 60% and 100%

- Blitz
V.A.T.S. Movement AP cost is reduced significantly and Melee Attacks ignore armor.  
To keep in the spirit of the vanilla perk the Blitz perks now reduce AP use while moving.   
Rank 1: Half AP cost and 15% armor ignore
Rank 2: AP cost reduced more and 30% armor ignore

-Iron Fist Rank 5
changed to work in Bullet Time V.A.T.S exactly like it did in vanilla VATS

- Gun Fu
Do increasing damage after each kill while in V.A.T.S.
The vanilla perk depends on a list of VATS targets. You don't have a VATS target with the common methods of turning vats into bullet time, so this perk didn't work.   
I changed it to kill counting because keeping track of the order actors got hit is too heavy on the script engine.
Rank 1:  25% more damage after your first kill while in V.A.T.S.
Rank 2: 50% more damage after your second kill while in V.A.T.S.
Rank 3: In V.A.T.S. you instantly do a Critical Hit against all targets after your third kill.

- Penetrator
Guns ignore target's armor while in V.A.T.S.
The vanilla perk allows shooting through walls. Outside vanilla VATS that is a on/off thing and creates unwanted effects like exploding bullets not exploding.
Shooting through armor is sort of like shooting through walls.
Rank 1: ignore 10% armor
Rank 2: ignore 20% armor

-Critical banker
Increases Critical Hit Chance while in V.A.T.S.
This is intended to work with the "Critical Hits outside VATS" mod. Since we cant bank crits, the perks now increase crit chance.
The 4 ranks are 4%, 8%, 12%, and 16%

-Quick Hands
changed to work in Bullet Time V.A.T.S exactly like it did in vanilla VATS.

How to use
This is important, read it.

After you load a game with the mod installed you will receive a settings holotape: [Settings - Bullet Time VATS]
It sorts to somewhere on the bottom of your misc list.  
If you did not receive the tape you can make one on a chem workbench. It's in the utility section.  

If you do NOT have a "Quest 2-like" controller you need to setup your VATS button in the settings holotape.
A quest 2 like is any controller that is based on the same reference design. Pico 3 and 4, Pimax Crystal, etc.
So if you use vive wands, index controllers, WMR, or anything else you need to run the button setup.

If you do have "Quest 2-like" controllers you are probably good to go. If needed you can always run the button setup.

Button setup:
In the settings holotape go to the VATS button Setup Menu.  
Follow the instructions you get to the letter.   
After the process is done a message box will report you controllers ID and your VATS button ID.  
Please comment with your controller model and those two ID's. I can then add those controllers as option to the tape, saving future people from having to do the button setup.

Setting up movement:
Setting this up is a bit unusual. In order for the script to be able to toggle between direct move and teleport it needs to know what your move settings in the game menu are. Unfortunately The script cant reliably retrieve your movement settings.  
Therefore you have to tell the script via the holotape.   

Go to the movement settings menu in the holotape. Here you find two options

"Outside V.A.T.S"
Set this option to match the movement settings you have set in the game options.  
So if you have the game settings set to "Direct Move", then the holotape option must be set to "Outside V.A.T.S" game movement option is set to: DIRECT MOVE

"In Bullet Time V.A.T.S"
This is where you set what type of movement you want to use while in Bullet Time V.A.T.S.
Direct Move or Teleport.

The other options:
-Time Dilation
Set how slow the slow time is

-image space mod
Choose from 4 options.
VATS green. A green tint like the vanilla vats effect.
Clarity. Increased brightness and saturation
Bookends. The beginning and end of VATS are marked by a green flash. In between there is no effect.
Off. Only sound marks beginning and end of VATS.

-ap consumption rate
Set a multiplier for AP use. The default is almost exactly like the vanilla VATS AP drain.

-use awareness perk
Did you get the perk but don't want the effect for any reason? Turn it on or off here.

-vats defence
Set the multiplier for VATS defense. The default is the same as the vanilla VATS effect.

install and Load Order:
Files go in data, as per usual. Don't forget to add it to your loadorder.  
Ideally this goes after FRIK. So you probably should not install it until after you exit the Vault.

uninstall:
In the holotape click on uninstall.
After clicking confirm, close the pipboy and save+exit your game.  
Remove all mod files.
Start game and load save. Uninstall completed.

Update:
In the holotape click on uninstall.
After clicking confirm, close the pipboy and save+exit your game. 
Install the new version.  
Start game and load save.  
You have to redo your holotape settings and possibly the button setup too.

Compatibilities and mods with "wrong" methods
Here I will try to keep track of what works and what doesn't.

DLC:
in theory it should work without DLC's, I just haven't tested it.

Mods that work well with this mod:  
Critical Hits Outside of VATS 
I consider this mandatory. My mod is not touching perks that this mod edits., and the crit changes I put in my mod are complimentary to Crits Outside VATS.

Hip-Fire Perk Replacers

Weapon Accuracy Redone for VR

Mods that do not work or are made redundant by this mod:
VATS Tweaks 
From this pancake mod most options are either made redundant or do not work in Bullet Time V.A.T.S.  
Slow time has options in the holotape, Mysterious stranger works, VR doesnt have killcams or VATS cams, There are no killmoves in VR, HIT chance isnt used in Bullet Time.

No VATS Damage Reduction 
Made redundant, the holotape has VATS defence options, including turning it off.

VR Neutral VATS
Redundant. The holotape has options for image space mods, including turning it off.  
However no problem if its installed, the mods do not change the same things.  
Do not go uninstalling this one halfway a playthrough. I have no idea what swapping out the main ESM will do then, so just in case I say: Don't.  
Letting it be is just fine.

Mods that use one of the problem methods:  
Anything that changes the following settings under the  [VATS] section in the ini file.   
fVATSTargetUpdateSec
fVATSShapeRadius
fVATSShapeLength
fVATSSightedEnterSec
bVATSForceRanged
bVATSDisable
fVATSPotentialTargetRaycastDist
fVATSInitialTargetAngleWeight
fVATSPartSelectDistanceWeight
fVATSOffscreenPartFocusDelay
fVATSPartChanceUpdateSec
fVATSTargetSelectSec
fVATSExitSec
fVATSEnterSec
fVATSTargetSelectMinFOVDegrees

Any mod that changes an internal game setting that is equivalent to the above mentioned ini entries.

No VATS Overhaul  
In pancake it disables VATS by setting fVATSMaxEngageDistance to 0. 
In VR that does NOT disable VATS, but only disables VATS targeting, and thats the problem for VR.

With thanks to:
Frazaman - Fallout4 VR Tools.
Rollingrock16 - some code in Fallout4 VR Tools, general tips.