So, I totalled the previous motherboard and found a new one online. This one was the 16mhz version (the original was an SX-20) and had a different component layout. At the same time, I also purchased 8mb of RAM (Parity SIMMs!) and a 'new' Dallas Clock Chip/Battery from eBay.
After slapping it all together, the RAM counted up nicely and I could get into the setup as per usual. I configured the HDDs and then saved the settings and rebooted. Instead of working fine, each reboot presented me with the 162-System Options Not Set-(Run Setup) error. No amount of configuration would work. Everytime I continued and went into the setup, it would remove the HDD configuration. I could see that the BIOS wasn't even searching for the HDDs.
This was weird as the system was more-or-less configured back to a standard Compaq factory-issue. Everything was in good nick. I had a hunch though; maybe that Dallas Clock Chip from eBay was actually already dead!? The fact that I hadn't powered down the system meant that the configuration should have applied; this didn't seem to be the case!
I replaced the battery as per the previous one that I replaced (I actually ended up using the original one on the motherboard for the other 386 I picked up recently.) With the hack in place, the BIOS configuration saved and the HDDs were detected and ... the world was a happier place!
So... if you have a dodgy old Compaq Deskpro like mine: MAKE SURE YOU HAVE A GOOD CMOS BATTERY!