Download B.A.E. - Bethesda Archive Extractor
Download JPEXS Free Flash Decompiler
Download my HUDMenu.swf so you can follow along

Use BAE to extract "Fallout4 - Interface.ba2" in "C:\Program Files (x86)\Steam\steamapps\common\Fallout 4\Data" 

Then open HUDMenu.swf with JPEXS (or just open my HUDMenu.swf if you just want to modify what I've already done).

The way I'm "removing" these UI elements is not actually by removing anything at all, but rather by moving it off of the viewable screen.  For the most part you'll only be editing things under the "sprites" section in JPEXS, and if you navigate to a "frame" and then a "PlaceObject", on the right panel expand the tree for "matrix" by hitting the plus sign next to it.  THE ONLY VALUE I'VE MODIFIED IN THE ENTIRE FILE IS "translateY : SB [nTranslateBits] = 42,000".  Anywhere you see "translateY : SB[nTranslateBits] = 42,000" is something that I have personally modified.

Below is a list of every single modification I've made, along with the default value for each in case you want to bring something back to the way it was.  Hopefully it's not too hard to understand, I wasn't intending on sharing these so that's why its a little sloppy.

HUDMenu.swf
449 - Right Meters
441 - Action Point Meter
-Remove "AP" text (sprite 441, object 439), default -120
447 - Ammo Count
-Remove total ammo and separator (sprite 447, objects 444, 446), default 0, 0
437 - Flashlight Widget
-Remove flashlight widget (sprite 449, object 437), default -4670
432 - Explosive Ammo Count
448 - Power Armor Low Battery Warning

452 - Bottom Center Group
427 - Compass Widget (276, 275?)
-Remove enemy markers (sprite 275, objects 274, 263, last object), default -300, -460, -140
451 - Crit Meter
410 - Perk Vault Boy
409 - Subtitle Text

406 - Left Meters
398 - HP Meter
-Remove "HP" text (sprite 398, object 395), default -120
403 - Rads Meter
405 - Location Text

459 - Center Group
392 - Quick Container Widget
-Remove button hint bar (sprite 392, object 328), default 3240
-Remove brackets (sprite 390, object 387), default 640
373 - HUD Crosshair
-Remove crosshair (sprite 372, object 371), default 0
-Remove crosshair animations: (sprite 370, objects 342, 351, 354, 355, 356, 357, 358, 362, 368), default 0, 0, 0, 0, 0, 0, 0, 0, 0
-Remove all crosshairs (sprite 372, objects 370, 371), defaults 0, 0
453 - Explosive Indicator (241?)
-Remove explosive indicator (sprite 235, objects 230, 232, 234), (sprite 237, object 236), (sprite 238, object 233), (sprite 240, object 239), default -8, 13, -1, 0, 0, 0
454 - Directional Hit Indicator (252?)
-Remove directional hit indicator (sprite 252, object 251), default 0
458 - Hit Indicator
-Remove hit indicator (sprite 456, object 455), default 0
334 - Rollover Widget
-Remove button hint bar (sprite 334, object 328), default 560

466 - Top Center Group
325 - Stealth Meter
-Remove stealth meter (sprite 466, object 325), default 1840
465 - Enemy Health Meter
-Remove enemy health meter (sprite 465, objects 319, 394, 397), default 480, 480, 480

471 - HUD Notifications Group
470 - XP Meter
313 - Quest Updates
310 - Objective Updates
309 - Quest Vault Boy
307 - Messages
306 - Tutorial Text
283 - Prompt Message Holder

VATSMenu.swf
85 - VATS Menu
46 - Button Hint
59 - Apply Critical
-Remove PipBoy animation (sprite 85, object 59), default 10800
76 - Four Leaf
-Remove four leaf clover animation (what's this for?) (sprite 85, object 76), default 11200
82 - Resistances
84 - Resistance Brackets

DialogueMenu.swf
22 - Dialogue Menu
12 - Question
12 - Neutral
12 - Negative
12 - Positive
12 - Speech Challenge Animation
-Remove speech challenge success animation (sprite 22, object 21), default 0

Uploaded file versions:
HUDMenu.swf - Default:
-Remove "AP" and "HP"
-Remove flashlight
-Remove enemy compass markers
-Remove button hint bar and remove brackets for containers
-Remove crosshair and animations
-Remove explosive indicator
-Remove directional hit indicator
-Remove hit indicator
-Remove button hint bar for objects
-Remove stealth meter
-Remove enemy health meter

HUDMenu.swf - with button hint bars:
-Remove "AP" and "HP"
-Remove flashlight
-Remove enemy compass markers
-Remove brackets for containers
-Remove crosshair and animations
-Remove explosive indicator
-Remove directional hit indicator
-Remove hit indicator
-Remove stealth meter
-Remove enemy health meter

HUDMenu.swf - with button hint bars, explosive indicator, direction hit indicator:
-Remove "AP" and "HP"
-Remove flashlight
-Remove enemy compass markers
-Remove brackets for containers
-Remove crosshair and animations
-Remove hit indicator
-Remove stealth meter
-Remove enemy health meter

HUDMenu.swf - with explosive indicator, direction hit indicator:
-Remove "AP" and "HP"
-Remove flashlight
-Remove enemy compass markers
-Remove button hint bar and remove brackets for containers
-Remove crosshair and animations
-Remove hit indicator
-Remove button hint bar for objects
-Remove stealth meter
-Remove enemy health meter