I got my additional Pi with FLIRC running in my home theater. It receives IR through the keyboard_remote integration successfully ! I used a guide from Controlling Home Assistant with an Old Remote – The Helpful Idiot to do it.
It took entirely too long to get to this point - turns out the X10 IR codes I was previously using don’t learn well into FLIRC. I reprogrammed my ARRX18G remote to a set of IR codes for a Daewoo air conditioner, and learned them into FLIRC. Phew.
Now, I’m left with sorting out the proxy part, with the Home Assistant remote add-on. My 2 HAOS nodes are connected to each other, but somehow no entities are being shared. And with the keyboard_remote integration, there are no entities anyway, just events … I may have to wait until tomorrow to deal with this.