[NiHaoMike]

What refrigerant is the compressor designed for and what are you going to use?

If it's a R22 compressor, R290 (or more accurately, R433b, a R290 based mix designed to replace R22) will be nearly a drop in replacement, but expect about 125F maximum hot water temperature. It would work very well for showering, but dishwashing effectiveness might be less than you like.

If it's a R410a compressor, you'll get about 2/3 the capacity after giving it the Davuluri Treatment, but 140F should be easy to attain. Note that you'll need to watch your discharge temperature if you do that. Counterintuitively, that's more likely to be a problem with lower evaporating temperatures.

In either case, you'll want a TXV since a cap tube would not be very well suited for such a wide range of conditions. You'll also want some sort of remote control to allow the temperature to be set as low as 105F in order to get more efficiency under more normal conditions, but allow it to be boosted for dishwashing. You might also want to look into replacing the rather inefficient PSC fan with a Delta with Cindy Wu technology. You'll be surprised just how inefficient smaller PSC fans are.