In the meantime I had to RMA my 1635s and got a brand-new 165P6S as a replacement. The 165P6S also gave me the 'DMA Driver Error' screen. As suggested, I moved my good ol' Teac W524E to the ITE controller and the Litey to the mobo controller. Everything works fine now. It seems my ITE 8212 controller likes older drives better.
Liteon 165P6S MS0P, Benq 1640 BSRB, Teac W524E 1.0E