You have to remember that when the C31 came out Pebbles and Bambam were stealing the batteries out of Fred's remote, it was really dinosauer times in the remote control world.
We would regularly program the state of the art at that time learning remote from Memorex, the CP4, to use in the main room with the clients non Mac CD, VCR etc and then the Mac remote would end up in a drawer or in a second loctation with a IR sensor. The big Memorex remote did not have the correct shift resistor code capability to command the Mac units.
That is why so many Mac units that come from estates are missing the remotes, they most likely were in the bedroom nightstand. There inside info for all the estate flippers out there.
There used to be a online clearing house that my installers used to use to find remote codes to use when they built up custom remotes for installations. That type of site and a customized remote is your best option in today's remote world.
You have not heard a c31 until you have heard a recapped C31, those caps used from the dinosauer days of the 80s really fell off quickly after their 20 year expected life span. Unbelievable how much broader, deeper and more detailed the soundstage can become.....did a number of A,B,C comparisons between a recapped C35 and stock c30 and C31..... the difference was stunning so we recapped them both to get them back up to their fighting weight and match the C35.