The hard part is figuring what your heat loss would be, obviously... and that is dependant on air and water temperatures, humidity, cover effectiveness... lots of variables. I'd try to find someone who uses their pool as you intend, and find out. I have neighbors in Florida who switched to heat pumps after their propane bills were $300+ per month in our mild winters. I imagine it is worse in Missouri because of the harsher winter. Is your health club membership that much?

I'm located in North FL. Last Christmas we heated the pool for a week while the grandkids were here.

Daytime was sunny and temps were 50's during the day and low 40's at night. We have a very small pool (6500 gal.) We heated to 82 degrees. We have a solar cover that stayed on except when swimming. It has to be rolled out manually and probably had some gaps.

The upshot is that the week cost close to $300 in propane. We haven't heated since!

We use our heater quite a bit in April & May and Sept & Oct. We tell our kids it's either the AC/heater in the house, or the pool heater cuz we can't afford to use both. It does get expensive! And when temps really start cooling off, the water temp doesn't stay very warm. I would think you'd have to run your heater a good part of the night & day to keep the water temp at swimming temps. At least with our pool, even with the auto cover, the pool doesn't hold the heat very well when the ground starts getting cold.