I has been almost proven beyond any reasonble doubt that the cause for the crashes it's not the Tekram SCSI controler nor it's drives.
Yesterday I had here a DC390U2W (which has a NCR SCSI controller chip) and now I have a DC390U3W (which has a LSI 53C1110 SCSI controler chip and the SYMBIOS SCSI BIOS) which make for to much different elements to have them causing the same error (random crashes whem moving a lot of files).
So I wen't for taking out 384 MBytes of RAM (down from 512 MBytes to just 128 MBytes) and slowed down the whole system;
FrontSideBus at 103MHz instead of 133MHz (which lowered the processor speed from 933 MHz to 721 MHz), disable all "advanced features" that could be making the crashes (they are just "shots in the dark" as so far I could come up yet with a reason for the crashes), etc.
And the system (so far) is stable.
So I'm going to finish the instalathion and then start enabling "advanced features" and speeding up the whole system to see how far it remains stable.
I hope that this way I can figure out the reason for all this trouble...
See you all later!