I fixed my card and manage to bypass Adaptec's shitty flash tool locks. Here's the deal:
Grab uniflash140 from the net.
Get the latest bios for your 29160 from Adaptec's website.
Run the self-extracting zip file and rename the .BIN bios file to whatever you like (I used backup.bin for the sake of simplicity)
Boot DOS from floppy or whatever means you've got to do it without XMS or EMM386 loaded into memory.
Run aflash4.exe or aflash5.exe -scan and take note of your cards' bus and dev number. Depending on which slot the card is installed, you'll get different numbers. My rig has an ASUS P3B-F and I have the 29160 installed on the 5th PCI slot, so the utility returns a result of bus 00 dev 13.
Type in uniflash -pcirom 0 13 0 (use the bus and dev numbers you already got from flash4/5 and add an extra 0) -e nameofthebios.bin.
In my case it looked like the following uniflash.exe -pcirom 0 13 0 -e backup.bin
Wait until you get a confirmation screen and press 1, then enter.
Wait until the progress bar ends and you'll hear a short speaker beep.
If everything went fine, you'll get the SCSI bios loading properly on the next boot.