Well, things are looking good! I installed Windows 7 and FSX (plus addons) all over again on the SSD (I am becoming an expert and very fast at it...

), making sure the other install of Windows 7 and this one are completely seperated: they can't 'see' each other at all now. I think something went wrong with that the previous time (when I could even run the same install of FSX on BOTH systems...!).
I loaded the Kodiak, no problem, started a flight, no problem, quited FSX and did it a few times all over again: no problem. Restarted the computer using the other Windows 7 install, went back to the 'FSX OS', still no problem. Switched the plane during a flight: no problem.
I didn't have time anymore to make a 'real' flight, only to load the Kodiak a few times, but up to now it's looking good... It's a pity I don't really know what went wrong, of course, but right now it seems to be okay. This evening and coming weekend I will make a few flights. Hopefully it stays this way!