Heater/Chiller Recommendations

Look at Aquacal or Built Right Heat pumps.

Check that you have local parts and service for the heat pump you get. Companies that sell heat pumps often don’t service them.

Heat pumps can be expensive to cool a pool. Consider a Glacier Pool Cooler.

 
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For an all-in-one solution, a heat pump with chilling capability works well. I have one and I'm happy with it.
 
A Glacier Pool Chiller performs poorly in humid weather. The company is out of Phoenix AZ and while they work well here in the desert, they probably will struggle in swampy Louisiana. A combo HP/chilleris probably the best way to go but be absolutely sure there are contractors around that can service it. Pool companies love to install equipment but very few know anything about HVAC service.
 
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For an all-in-one solution, a heat pump with chilling capability works well. I have one and I'm happy with it.
What brand do you have and what size pool? I had one quote for a Hayward at 8800.00 and then I would have to have an electrician come out to do electrical at additional cost
 
AquaCal heat pump. 21k gallons. (Both are in my signature.)
Just as a point for comparison. Our pool is half the size of yours and we are in Lake Charles, LA. We seldom use our gas-fired Mastertemp 400K heater but used our Glacier GPC210 chiller daily last summer. Our pool gets little shading during the day, has almost white plaster and would reach temperatures of the mid-90s during the heat of the day. By running our Glacier chiller at night, it would drop the temps 8 - 10 degrees which brought the water temps into the mid-80’s which was perfect for us. I know Glacier makes a larger chiller which you may want to look at for your larger pool.

Good luck on your decision.
 
If live in a climate where installing a screened enclosure over the pool is possible, this works extremely well for controlling pool heat in the summer. Screen knocks down UV rays by over 50%. Here in central Florida, my pool never gets above 90 in the summer due to my screened enclosure. The neighborhood pools that aren't covered hit high 90's during this same time.

My pool in GA was similar - I couldn't have a screened enclosure because they still get ice and snow which would have collapsed the screen. My pool there regularly hit temps in the high 90's. I installed sun shades over the pool, and that dropped the temp significantly - into the low 90's. 91 or 91 feels pretty good when temp is over 100 out.