I have had to order a number of parts to work on these issues and they all arrived today. Progress so far:
First thing I did was replace the 68030 CPU with a nice, used ceramic-packaged 01F91C which I bought from a reputable seller. This had an immediate effect of being able to boot the computer from the Buddha IDE / SD adaptor with the BigRAM board installed. I was also able to boot into AmigaTestKit v1.18 on an ADF image using my GoTek external drive. By the way, I'm now suspicious of the original chip in my A2630 - the FPU is ceramic, why would the CPU be plastic?
After changing the CPU, running the memory test got me optimistic but... after about a minute, it crashed with illegal instruction exception much like above. I rebooted a few times and tried different memory tests - including just the chip RAM - and eventually got an exception each time.
Next, I recapped the power supply. This wasn't too hard, the board is all through-hole and very easy to work on. Other than a sense of accomplishment of not breaking it, there was no improvement to the memory tests. Illegal instruction crashes continue.
I'll note that although I can boot into the Workbench, eventually corruption starts creeping in and strange things happen. I tried running Basilisk II with MacOS because that's an app that can allocate a fair amount of memory, however eventually everything crashes.
The blinking power light is still going on. I followed the schematics and changed a transistor that controls it with no change. I haven't done it yet, but next up is changing the 74F08 that is next up the chain. I don't think I should be concerned about this as it relates to the BigRAM as it's just the LED; the 5V rail is rock solid.
So that's where I am. I now have a ITX power supply and I'm waiting on an adaptor cable for the Amiga to try out a completely different power supply.
In the mean time, is there anything else that I should be testing or doing?
And is there a chance that the BigRAM might actually be faulty here? How would I know?