I finally got it!
Thank you all for contributing to this thread and helping a fellow multirotor-addict not loose his patience =)
For anyone that suffers the same problems, this is what I've done to make it finally work (I will describe the whole way since I can't say what made the difference for sure):
I wanted to downgrade to software assistant version 1.2. The main reason: There are different people on the net who had the same problems as I had with my naza after updating to 1.6 and above (the same for the according newer firmware). But with version 1.2 their Nazas worked fine. So i got the 1.2 assistant, as I've read installing this assistant and then clicking on upgrade firmware would actually downgrade it.
This didn't work for me. I was not able to downgrade it this way.
So I shortened the Naza (connect F1 to F2 with a servo cable) and powered it on in order to reset it. This didn't work for me, neither. Connected to the 1.2 software assistant it still insisted on my Naza having the newest firmware and wanted me to install the newest assistant (1.8).
After all, I started the most recent assistant software (1.8) and plugged in my Naza. Wait a minute - no strange beeping on the ESCs this time (see first post). On tools -> firmware upgrade I clicked "Try again" and installed the most current firmware again. Calibrated my Tx, hit "write", disconnected the Naza, restartet TX + Naza w/ RX, then the CSCs worked perfect.
Can't really tell what was wrong, but since it's allright now I'm far from compaining. What a happy night.
Thank you again,
EE