Sounds like a very fun project
In regard to hacking an inverter-based system, I suppose the targets would be the compressor and the digital expansion valves. So first you need a "brain" to run the system, maybe an arduino or a pic or whatever is desired. Then you need to interface it with the compressor and valves. The thermistors and what not can be ignored and use your own if that's easier, rather than reverse engineering them as well.
The compressor may have its own dedicated hardware controller, as I'd imagine the compressor manufacturer wants to sell its unit to other vendors, and the simplest way would be to dedicate a cheap controller and provide a simple interface for controlling the compressor. In that case, you need to decode the communication protocol to that controller. This is probably the most difficult hurdle. Maybe something here..?
Inverter Control Module : Hitachi Appliances, Inc.
The valves should be really simple to decode, I think a youtube video described them as acting like stepper motors. They probably just have a reset command and positioning commands.
Once you have that down, I'd start the software with safeguards to protect the compressor. Then write up a test suite to go through various possible control schemes, and use sensors to measure efficiencies of each. Developing good theories and automating testing here will get the setup optimized quickly. Sensors can be integrated as desired to meet theoretical operation..