heat pump comparison

We are looking to replace our old EUS heat pump that has died. We are looking at three models. We hope to get some feedback. The three units in question are:

Rome 105Ti 105K BTU's 6.3 COP $3095 delivered
Solarium 105Ti 105K BTU's 6.3 COP $2995 delivered
Rheem 96K 5.1 COP $2495 delivered

I believe the Rome and Solarium are basically the same unit based on spec and pictures. The Rheem has a real nice price, but we are concerned about the size for our pool. Our pool is a 20x40, 30K gallons, i/g Roman style with cover. We keep the cover closed anytime the pool is not in use. We open the pool in mid-May and close it in early September. My wife likes the temp to be around 87-88 degrees and the starting temp in May is usually around 60. We live in Indianapolis.

Thanks for the input.

I know nothing about the units, but know a bit about math. The 105Kbtu unit will raise the temperature of the water by one degree in 2.383 hours while the smaller one will raise the temperature one degree in 2.606 hours -- not a big difference.