The recommendations to up your processing temperature are good ones, as it helps in keeping heat gain to your ambient tmep to a slower gain rate. I try and process at 72 to 74 deg and have never had a problem. In fact I just read a magazine article not too long ago, maybe in Photo techniques(?) about the fact that increased developing temps are not harmful. Your 80 deg ambient temp tho is a mystery to me if you have a/c in the house. I've used a 5000btu a/c unit, $89 + tax at the local appliance store, in my window which helped, but the thermostats are not pin point accurate. They have a range of 3 or 4 degree's, but I was able to maintain much better temps in trays. Watch tho for light leaks thru the unit. They have to be sealed, and it is oft times a hassle, and I had to do my processing at night when the sun was down.
Since you are using a slosher, you have your hands tied a little. What I have done for long stand developing times for LF film is to use a Kodak rubber deep tank with water on the tiled floor. More water, more mass and it holds temps longer. I've successfully used 30 to 45 minute stand developing times without a problem, even with a slight drift. At these times, and if you are diluting your developer, the temperatures within a small range don't appear to me to have a great effect. The problem is, I usually only develop 1 sheet at a time in 2 stainless containers set in the larger tank. Developer quanities can be small and can be one use, and this is why I use this setup. (Whatever you try with water, do your test first and check your thermometer). With the slosher you have trays, so your setup is larger and complicating things. When I think about it, it would almost be more practical to lose the trays and go deep tank with hangers, depending on film size. That's what I did with 4x5 film in the beginning and it was a setup that worked very well. I used floating lids and keeped three containers setup on a counter all the time. I chilled only the developer in the refer and kept the a/c on to cool the area. Just a thought.
You can also try and find a Patterson Orbital processor. They are light tight and can process either 1-8x10, 2- 5x7 or 4-4x5 sheets when set in a water bath that can be maintained by adding ice cubes. This is by far the easiest method to employ for long times with LF film. They process film perfectly when used manually. Rough up the inside floor tho with some sandpaper so the film doesn't stick.