To whom it may interest:
The problem was solved by deleting(!) the ~/.gnupg/scdaemon.conf …
I still don’t understand, why the Nitrokey behaves that way with those 2 configuration settings (disable-ccid and pcsc-shared) but after deleting the file, the NK works reliably for the past 7 hours on those computers. The main competitors keys had no problem with that.
However, my problem seems to be solved. The RSA4096 performance of the NK3 is really REALLY slow but that’s something, I can barely live with.