TXV can be used on the 3rd stage if you either buy a dedicated R14 TXV or you regas the bulb on a TXV with an R14 charge. There's a thread or two here on the procedure but I can't remember who did it.

I echo DetroitAC's sentiments on 240VAC. For a 500w load you are looking at a multiple kW load on the 1st stage which would be difficult to shift with the current limitations of 110VAC compressors.

Sounds like a fun project and I hope you guys keep us in the loop. Always fun to see non-overclocking cascades in action.