I think I may have found the reason for both the DirectX error and the issue with the disappearing models (finally!).
The DirectX error appeared frequently today (prior to that I changed some stuff here and there, in the code and other content files), and after stripping down some levels (including the problematic one) and some other hub world related stuff I figured I should have a look at the jetpack. I re-saved the model and halved the skin size (thus re-saved the texture, too) and every error now seems to have magically vanished!
However, I fear the cause for the issues seems to lie somewhere else and I have just postponed the next error again (esp. because now using the old texture again does not lead to an error, I may try to use an old model file from a backup and see if the model was the faulty file).
I... I don't understand it, now the DirectX error appears every time again. This sucks.

EDIT2: Crashes after loading an almost empty level (1 block + player character) but doesn't after loading the complete first level. I have no idea how I am supposed to find and fix this issue.

EDIT3: I had low hope but I tested it anyway, it's not PC (config) specific, it crashes on my laptop, too.