So, an update.
I finally got my system up and running with the GA-586HX and so far it seems stable, but I first had a bit of an adventure with disk-on-modules. A lot of my retro hardware is currently in inaccessible storage due to renovations, so I only had one sub-2 GB HDD on hand, an old Conner drive in my Compaq Deskpro. I intended to use a DOM for this build anyways, so I wasn't too concerned, but I only had two 40-pin DOMs, the rest were 44-pin. The first was an old used US-made Simpletech 256Mb module, the second was a new 2GB LeiDisk I ordered from China for this build. After the LeiDisk arrived I opened the plastic clamshell case out of curiosity, and I was glad I did. I've never seen such shoddy SMD solder work before. There was even a solder bridge across two components, which fell off when I poked at it. I plugged the thing in anyways, expecting at best nothing and at worst smoke, but the computer recognised it. I installed dos with no issues, but that is when the problems started.... every other IDE device, whether on the same IDE interface or the second one gave me problems. CD-Rom drives would be recognised by the system, but I got I/O errors when I tried to use disks in them. Floppy disks that I knew were good wouldn't work in this machine. Sometimes on post the names of the drives would be garbled and the system would hang. Seeing as this computer had sat in a damp basement for almost 20 years I was starting to think there was something wrong with the motherboard, but I decided to pull the Conner from my Compaq to test it. With the Conner installed everything ran fine but very slow. So I decided to give the Simpletech DOM a go. That module had been tested, set up, and loaded with software with an old XP box, so I knew it worked. But when I put it into this build, while it was found by the BIOS, the computer gave me an I/O error and would not boot off of it. If I booted off of a floppy, I could access the Simpletech DOM with no issues and all of the other IDE devices worked fine. I messed around with BIOS and jumper settings for a while, and was about to give up when I decided as a last-ditch attempt to try FDISK, delete the partition and re-initialise the DOM, and success!
I'm really pleased with just how super-fast the computer boots with the Simpletech DOM. Everything is really snappy compared to running the system with the old HDD. Now I just have to do something about all the rust on the case...