IvanT: The E32/E34 HVAC/IHKA control unit has quite a different internal construction despite the very similar looks. You will not find suitable donor parts in it. This eBay auction has a few pictures that clearly show the different button mechanisms.
If you are brave you could try to disassemble the buttons. These old style buttons often share the same switch mechanism for momentary and latching switches with an external spring/latch being the difference. Maybe that broke or came dislodged. Sadly I can't say for sure this is the case with the HVAC control unit buttons. It's been many years since I had my HVAC control unit open. I don't remember all details but I do recall that I could not get access to the individual switches due to the metal brace over them. I forgot how that brace is attached but I think the only way to get access to the individual switches was to desolder them from the PCB (which I did not attempt). If you'd like to give this a try you'll need a proper desoldering iron/gun. Solder wick or a solder sucker won't do the job. There's a lot of pins to desolder and these old PCBs are easily damaged (traces and pads lifting) from excessive and prolonged heat. Even if the switches do not have an external latching mechanism (or it cannot be repaired), you might be able to locate the manufacturer and part number. Maybe replacements can be found. Anyway, there are a lot of uncertainties here. There may not be an external latch, it may not be repairable, and the switches may no longer be available with no suitable replacements.
If you decide to replace the RHD control unit with a LHD version, the passenger-side roller wheel indeed becomes the master (overriding the driver-side roller wheel when set to the maximum/minimum)? If that is annoying/undesired you can simply desolder the passenger side microswitch and move it to the other side. If you look at the PCB you'll notice that the solder islands and switch outline are present next to the other roller wheel.