Didn't forget about this!!
A fair few things have changed - in hindsight, maybe too many in one go but I was trying to make the best use of my time - but sadly I'm no further forward than I was before...
The first thing I did was replace the Super I/O chip as I confirmed that was dead. After replacing it, I found out that the person that gave me the computer originally did actually have a PS/2 keyboard, so I decided to wait to turn it on until I got that keyboard to rule out my RPI hack job as a possibility for being the cause of the issue.
While I was waiting to get the keyboard, I also found a listing for 2x of the southbridge 82371FB chip, so I bought them and decided to also replace that chip on my motherboard, given the possible PRI IDE channel failure. It went well, compared to the first time, and multiple visual inspections with magnification didn't expose any solder bridges. I then, to rule out transient voltage issues, recapped the power supply and the two electrolytic caps by the VRMs.
Eventually I got the keyboard (Sunday), and tried to turn the PC. Thankfully nothing catastrophic occurred, but it wouldn't even POST at first. After another visual inspection I did find a couple solder bridges on the southbridge chip (I've no idea if I missed them the first time or if somehow maybe I caught the chip while doing the recap ¯\_(ツ)_/¯) but after fixing them it did POST. Sadly, it got no further than before, reporting not only a floppy controller error but still failing to find any bootable media. I've got a couple things I'm going to try over the next few days, worst case even replacing the chip a second time, because perhaps the shorts caused the issue, but if that proves fruitless then I think I will have to consider that a defeat.
With all this fiddling I've done it really could be anything, maybe I've damaged the northbridge, some other component, IDK, and without a datasheet of the motherboard though I think I'm really at a disadvantage. If anyone has any ideas since it can at least POST now then let me know (P.S. the HDD isn't detected in either the PRI or SEC slot).