Thanks for the info. Here is an update.
I discovered an Adaptec 39160 PCI card in my ancient hardware collection with a bios date of 2000. It is a 64 bit card, but works without any problems in a 32 bit PCI slot. The card I mentioned previously plugged into a PCIe slot, so maybe that is why it would not work. I ran some disk r/w tests overnight without errors. Just to be safe, though, I think I will clone my SCSI disks to some SATA disks and retire the drives. They are very fast (15K RPM), but only hold 160G. Kind of a joke by today's standards.
The main message here for future reference is that the Adaptec 39160 is compatiblewith the DZ77RE-75K.