I have the exact same cooler, but mine is the Xtreme 6 version (supposed to keep ice for 6 days as opposed to 5, so presumably a little thicker insulation). I've used for multiple batches over years. What I do is heat my strike water to about 170-175, then allow that to sit in the cooler for 10 to 15 min. After that I check the temp, and if it's still too hot, I stir with the top open until I'm down to a degree or two over my calculated strike temp then add the grains to the water. By the time I've stirred out the clumps, I'm at the strike temp, and close the lid. I've never lost more than 1*F over an hour or more with that process, and that's even with pretty cold ambient temps. FWIW, I use a stainless braided plumbing hose as my sparge manifold, with a copper wire coil inside to help it keep shape. I've never had any sparging issues with that.
I will say that I originally went the 70 qt route because I was thinking I might do 10 gal batches at some point, but I haven't done that yet. Still, it works fine for me for 5 gal, although I freely admit I could've gotten away with a 50 qt size for what I've actually been doing to this point. The 70 qt size would also allow me to do a much bigger barleywine/imperial stout than I would've been able to do with a 50 qt, but again, I've never actually brewed one of those either!