Ok, it works! 
The problem was, that I set register 2 to #00 instead of #1f. I thought the bit 0-4 are not used in screen 6, but if I didn't set them to 1, the VDP repeated the screen data every 40*24 bytes.
Thanx a lot for your help! Now I can start with some tests (but not today...).
Have a nice evening!
Hm, I couldn't stop. Logical Copy made it to about 2500 4x8 blocks (this is the average size of a char in SymbOS) in one second (I hope I didn't make a mistake). This is about 1,7 times faster than on the CPC! I hope the final routine won't be much slower, but as the Z80 and the VDP can work parallel I don't see a big problem here.
Hehe. When you're on a roll, it's hard to stop.
That's about 40k/s. Sounds about right. The parallel processing should be helpful indeed. Even with those small copies you can set up the next character while the vdp copies one.
