If you wanted to stay with a SBC type setup, you could always look for a 486 SBC with ISA and PCI. I finally snagged one for a good price a while ago. A few different ones were made. If you look on eBay for sbc-490, an expensive one will pop up.
The one I bought was an Advantech PCA-6149.
There is one on eBay right now, but with shipping it is over double of what I paid. (I paid $60 plus maybe some shipping). Maybe shipping is cheaper for you though.
The max number of PCI slots that is supposed to work with these is 4, so I also grabbed a backplane with 4 PCI slots and the rest ISA.
It supports everything from 486SX up to POD83. Unsure if it will work with Cyrix 5x86. It does officially support the AMD 5x86.
See here for the manual:
http://support.elmark.com.pl/advantech/pdf/PCA-6149man.pdf
It is probably the best 486 SBC you can get. It has Tseng ET4000/W32 connected through PCI for the video and VLB IDE.
So yeah, it is a pretty sweet board.