You could switch to 4 wire, but without my being there to see exactly how all is wired, would not be easy to explain the wiring changes necessary.
I would advise a Tech for that.
The two wire t-stats work fine, you just have to set for heat or cool at control box instead of t-stat.
Also, IF the 2 wire t-stat has a heat-off-cool switch on it, be sure it stays always set to heat, even in cooling season.
Your a/c is controlled by the control box reversing relay inside.
Does your 2 wire control box have a wiring diagram on the box or cover ?
Take care and best wishes,
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