Update 4/18/2021: Uploaded a combopatch (BluePalaceTerrace-LOTD-JKsBluePalace-Patch.esp) for BPT-LOTD-JKsBluePalace combination as well. This depends on the BPT-JKsBluePalace patch here, as well as my BPT-LOTD patch (BluePalaceTerrace-LegacyOfTheDragonborn-Patch) from Modular Blue Palace Terrace and Solitude Patches. Load order between patches probably doesn't matter as long as dependency order is observed. In my test environment my order is as follows:

• LegacyoftheDragonborn.esm
• BluePalaceTerrace.esp
• JK's Blue Palace.esp
• BluePalaceTerrace-LegacyOfTheDragonborn-Patch.esp
• BluePalaceTerrace-JKsBluePalace-Patch.esp
• BluePalaceTerrace-LOTD-JKsBluePalace-Patch.esp
  

With this setup, side gallery of BPT is moved into an interior cell, and gallery door to Solitude city has been moved inside the blue palace courtyard. All doors involved has been tested with a follower in both directions to ensure navmesh integrity.

Make JK's win everything in the SolitudeBluePalace Cell

I resurrected the script I used to build my BPT-PCE patch, and updated it with some new knowledge. With this script I built the initial state of this patch. It has the following logic:

 - Iterate through all BPT records in SolitudeBluePalace cell
 - Any record that is a vanilla record touched by BPT, but not touched by JK's - restore the data back to vanilla record
 - Any record that is a new BPT-added record - disable it.

Specifically, "disabling" meant the following:

 - If the record is a navmesh record, set "Ignored" flag (the logic had this part but it didn't actually happen on any records in this problem)
 - Otherwise, set "Initially Disabled" flag, and Z to -30000
 - Additionally, if the record is a PortalMarker, remove any XPRM (primitive) and XPOD (portal data) field data
 - Additionally, if the record is a RoomMarker, remove any XMBO (bound half extents), XPRM (primitive), and XRMR (linked rooms) field data

Then, I ran this script on BPT version 0.9. I needed to run this on version 0.9 because version 1.0 added a bunch of NPCs and markers that are integrated with AI packages, which I don't yet know how to programmatically deal with. Naively running the above script on BPT 1.0 results in a Blue Palace interior that crashes if you enter a second time, so we gotta start with 0.9 and then hand-update to 1.0 after we get 0.9 working.

The immediate result of the above is that if JK's is loaded after BPT, you get a SolitudeBluePalace cell that is 100% JK's, and 0% BPT's. Everything BPT will have been disabled, reverted to vanilla, or lost the conflict against JK's (because we load it after).

Integrating BPT doors into JK interior

Then, I resurrected the following 3 doors from the disabled records:

 - BPT xx00A895 (palace door to BPT terrace)
 - BPT xx017603 (palace door to BPT side gallery)
 - BPT xx032820 (palace door to BPT basement)

And for each of the above doors, I found places in JK's Blue Palace to restructure the walls a bit and put the doors there.

 - Door to terrace is now located in the left corner of JK's dining room
 - Door to side gallery is now located over in a small new corridor near door to Pelagius Wing
 - Door to basement is located at the end of the downstairs hallway, where there is now a new flight of stairs that descend one more level leading to this door

For the small new corridor and the new flight of stairs, I added new Room Markers and joined them with existing ones nearby. In addition to the necessary "wall to door" type of changes, I also needed to relocate a bench, an animal head, and a lamp slightly to the side for the basement stairs so that they are not in the way. Also, navmesh has been extended. The doors are then finalized onto the navmesh.

Courtyard Navmesh

JK's Blue Palace added two doors to the palace wings that open into the palace courtyard. BPT remodels the courtyard, so BPT's navmesh was made to win the courtyard, with JK's door triangles finalized onto BPT's navmesh.

JK's Blue Palace also added a very clever patio thing above the gates. This did not require any work because the space fitted into BPT's new palace model perfectly, and the navmesh involved are completely standalone.

Integrating BPT NPC content into JK interior

With the above, I had a patch that fixes everything between JK's and BPT v0.9, which means it's time to bring in BPT v1.0's content. The difference between v0.9 and v1.0 are new guards and a new priestess NPC.

The priestess sleeps and eats in the palace interior, so a marker that denoted "this is where the dining room is" has been moved over to JK's dining area. The priestess's sleep area was a vanilla location that JK's did not change, so nothing was needed there.

The guards needed their spawn points and associated patrol markers moved to locations that fitted into JK's layout.

There's also a pile of firewood, that seems to be associated with the new gardener added in BPTv1.0, that I moved over to just outside the door leading to BPT basement.

The last thing that needed to be done for BPT is that BPT had a marker attached to a script for moving the throne object to where it should be. This needed to be disabled. I also removed the script on the record in addition to disabling it just to be safe.

... and with that, all conflicts should be patched.

Testing

To test, I took Belrand with me and exercised every single door involved in the patch and made sure Belrand could follow through in both directions.

Then, I stalked the priestess and the gardener's daily schedule and made sure there are no hiccups. I never really observed the gardener using the pile of wood, but oh well, he does not seem broken. I did not do the same for the guard because the conflict resolution there was fairly simple (just move some markers), so I'm just trusting that it works as long as navmesh is good.