Ok, I think I bring good news towards Windows 10 with 7435 and update. I have played for a bit over 3 hours with no faults now.
I have talked to Miguel, Carlos, Ira, taken over the airport. Talked to several AIM members through the website.
I also loaded an old save from my windows 7 machine, and continued from there a bit, talking to NPC's and a few battles. No problems.

Here is how I got it running:

First I also got a black screen i fullscreen mode. Then I changed to windowed mode, and i changed the compability of ja2.exe:
Run in XP sp3 mode.
Reduced color 16 bit
Run as admin.

I also set win 98 compabitly mode to true in the INI editor. (Might not be needed).

Now I got in the game, but I kept getting "Assertion error" or something similar.
Then I added the three DLL files from the "win8 fix".
ddraw.dll, libwine.dll and wined3d.dll and put them in my JA2 directory.

Now it runs perfectly, both in windowed mode and in fullscreen.