I probably should have added an update to this thread some time back..
I spent most of 2016 testing all sorts of things, looking into clues to figuring out solutions to the NEC-D780C compatibility issue.
Throughout 2016 I built prototypes trying out all sorts of parts from different manufacturers, made slight changes to the timing in the microcontroller firmware code, etc... Every now and then a Remix kit showed signs of improved NEC-D780C compatibility and I took note.
By the end of 2016, compatibility improved bit by bit. If I used exactly a certain combination of parts from certain manufacturers it started being NEC-D780C compatible.
At the start of 2017 pretty much all Remix kits I built were NEC compatible. Around DK Jr Remix's release, all Remix kits were NEC compatible.
Right now, even if some DK Remix vendors might still state they're not compatible with the NEC-D780C on their web site, they actually are.
It took time to work out all the clues because of the complex interactions between different signals across different chips from different manufacturers, but even the NEC-D780C plays nice now.