Are you located in Puerto Rico? Other's located outside North America have reported sync update issues. There was some question if sync OTA updates are available over seas. @Ducati1098 or @flip may be able to shed some light on Oasis and FDRS.
I guess they need to confirm what was found...big chunks or just flakes? It's been pretty well documented that these diffs generate a lot of metal flakes. IMO Have them change the fluid and go on your trip. FWIW this will still be covered under your powertrain warranty.
Perch collars are definitely a better option than the spacer pucks to reduce impacts to steering geometry however you will have to disassemble the coil overs to get then installed.
The negative should be connected to the frame or other suitable ground location...connecting directly to the battery post will bugger the battery management system. This is detailed in your owner's manual.
EDIT: Possibly misunderstanding...I'm referring to the Bronco battery post for charging.
Is the charger compatible for AGM charging? How are you connecting the charger to the battery? The negative should not be connected directly to the battery negative post.
Here's an old thread hacking a 2.3 muffler.
https://www.bronco6g.com/forum/threads/modded-stock-2-3-muffler-for-more-sound-video-sound-clips-added.67056/
To prevent bad CV angles, IMO, the lift should be as low as possible to clear the 37s.
Ride height has no affect on droop. Droop is the result of your coil-overs being fully extended. If memory serves the OEM squatch Bilstiens fully extended are +/-23.4". Most say you can go another inch fully...