Could both your 3.5 drives have gone bad, or the disks? Although disks are less likely since it should at least try to access them if they were bad...
Well the one longshot I thought of was maybe the power supply is spiking the voltage initially and that killed all three of my 3.5" devices. Maybe there's actually nothing wrong with the boards; maybe it's the PSU that fried the drives. But they all have power on all the pins they should, so that would seem really strange. Also, the Floppy Emu still passes its self check and it's getting power too. It seems really unlikely that any of them aren't working.
I've really only got two things left to try. One is really simple and that's just to check the PSUs for shorts. I just forgot to do that before, but that's a moonshot. I highly doubt I'll find anything there, but I just want to be as thorough as I can. I've checked them now every other way I can without taking them fully apart, and they seem fine to me.
The second thing, suggested by Steve at BMOW as his last idea, is to hook up an oscilloscope to pin 4 on the smartport connector and see if it's stuck in either low or high mode (it's supposed to be switching back and forth on boot to check if there's a drive there). If it is stuck, that would at least explain what's happening, though it wouldn't really explain why.
I've tested literally everything else multiple times now. I have no shorts, and I have good power everywhere, on the board and on the drives (and on the floppy emu). So I don't know what more I can really do.
When I get the new board I will absolutely test everything on it the same way before connecting anything to a) see if there are any differences to my current boards that would explain why my current boards are acting this way, and b) to give me a baseline to test again as I connect each component. I'm going to test with each component individually and only then start adding iteratively. If something does go wrong, then I should at least see what caused it. But hopefully nothing will.
You know, I try to be careful with my stuff but it is also possible that this is my fault. At least a couple of times I know I have unplugged drives from the computer when it was on. It's especially easy to do when it's taken apart like this, because there's just that one little LED to tell you that it's on, and the IIGS itself has no fans or other moving parts. So I need to be more careful about that.