Thanks to those who have helped out so far.
I don't know if what I just did is good news or not:
I put the flash card in a Dell GX110 instead, and did an installation onto the flash card. It took a little time, but it went through without a problem.
I took that flash card, and put it back into the GX260 and it booted up. I walked away from it for a little while, and I had the following message on the screen when I came back.
ad0: timeout - write_DMA retrying (1 Retry Left) LBA=5665679
I'm thinking the GX260 doesn't like something about the flash card, or something is still enabled in the BIOS that I don't see.
I rebooted the GX260 with the flash card and disabled the DMA and ACPI again. I'm gonna keep watching it and see if the error comes back.