HomeAutio.Mqtt.Harmony VS SmartIR

I have written several MQTT bridges for my own use, including one to Harmony Hub (https://github.com/i8beef/HomeAutio.Mqtt.Harmony). I bring this up, because I think the MQTT topic approach I use here could be a good example for you as I support the full gamut of options exposed by Harmony, which should be a pretty close approximation of your problem space.

SmartIR has a lot of mistubishi codes listed. If you go with a Broadlink RM4 Pro S or Mini S (S for including the temp sensor) you may be able to use it like a thermostat via IR commands, but in the worst case, should it be unsupported, you can still do the manual learning process for each of your remote’s buttons for some manual control with no UI feedback, then make some crude automations coupled with the temp sensor readings.

check out https://github.com/smartHomeHub/SmartIR

Just click on the Custom repositories option, and use the following link to fill the repository field https://github.com/smartHomeHub/SmartIR (make sure to choose Integration in the category list).

Do you use Home Assistant? If so, take a look at SmartIR, which will create a series of switches for the various speeds.

This is a shot in the dark, but there's a HA component called SmartIR, which has codes for various TVs. Here's one that references dedicated HDMI inputs, maybe they'll work

For example, my AC has four fan modes (low/med/high/auto), three operation modes (cool/heat/dry) and temperature range from 18 to 30 degrees. So, I had to record every combination of these three parameters (that means 4x3x13 commands + OFF command). See here.