Since this remote control unit (a UTB-YUB/GUB/TUB) doesn't have infrared, I couldn't just point an IR blaster at it. After some googling, I found a number of installation manuals and discovered the remote uses some sort of 1-wire (as in an actual single wire, not the protocol invented by Dallas Semiconductors) to do communication.
A few ebay searches later, and I found new remote control unit for $60 (from a supplier 20 km away), so I have a test unit that I can play with.
First step: Work out how this thing comminucates with the outside unit...
I've managed to get @jaroslawprzybylowicz code working with the 1-wire protocol, and ported to an Arduino lib if anyone is interested - https://github.com/unreality/FujiHeatPump
The wired remotes just need a LIN transceiver to split the signal wire into RX/TX.