re-wiring/retro-wiring a Carrier 40MVC024 ductless A/C for external thermostat: guidance
So per ThreePhaseEel's advice I've gotten a USB-UIRT and a couple blasters.  First impression of the guy who builds/supports them is excellent--great communication, answered plenty of questions before I even ordered, several more afterward.

I still need to pull/audit the codes from the remotes, but I'll update this answer as I progress.  Warning: my time is limited, so this will go slowly.

Anyone is still welcome to answer my original question.  It may not quite be an XY problem, but it's definitely a grey area therein.  If No one answers my original intent before I resolve via the IR workaround, I'll accept my own answer after updating it appropriately.

To be continued...