There are standalone control boards for doing what you want to with what have you. I have found that it is a lot easier to replace the control box than to assume control of it. The stuff I have been using is qunda brand. They also make remote controls for the consumer aftermarket and other digital controller modules than just for heat pumps.
I have seen they make an inverter compressor control, but I've never had or rigged one up. The magical machines I have built have all been constant speed.
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