Well, I have switched the whole tape mechanism between these two VCR's now. I still don't know if every single part is 100% identical... but it looks identical, it fits ...and "Holly Moses", IT WORKS!!!
The tape mechanism from the HR-S6600EU seems to work really fine in the HR-S7600EU. I've tested with playing a few tapes now, and both image and sound quality is really great... and the TBC/NR also seems to work fine :-)
This really feels like I have got a brand new JVC HR-S7600EU!
I hope this experiment can be usefull for others also, cos I guess it's really hard to find a HR-S7600EU in good condition, but it may still be possible to find a HR-S6600EU in good shape :-)