A friend called form the road delivering trailers. Truck was heating on hills. No codes and it would engage and he could hear it. Got a Doorman replacement clutch from one of the generic parts stores. It helped but still running hotter than normal. Told him to get a dealer part as I suspected from other experiences the Doorman was not quite the same. Swapped in the factory replacement and problem solved. The fan noise was much more pronounced under load also. Even though it will enage and there are no codes the fan never locks solid and the fluid coupling will deteriorate until it doesn't pull enough air. Its like a TC, not all fluid couplings are created equal. Thats been my experience when thermostat is good, rad is good and clean. The one caveat I have seen is a cracked head will drive the temp up and it is hard to determine of the excess heat is causing fluid loss or the pressure.
A shift kit may clean up the shifts if it is the apply pressure causing the lag and a flare. You say it is flaring into OD, is that before or after the TC locks, and does your TC lock almost immediately after the OD shift or wait a bit? Under a heay load and throttle with extra power the stock TC will flare pretty badly when you hit OD. Under normal driving it should not. The big question will be is the flare related to the TC or the OD clutches. A shift kit will not compensate for wear but it may cover it up with higher pressures. A flare into OD can be clutches, pressures, or just the TC. Really tough at times to tell.
I would do a shift kit, gov solenoid (the GM stle conversion), new transdcuer, billet accumulator, billet front servo, billet band strut and anchor. Then test the charactersitics afterward.
I would not do a TransGo kit if you are not intimately familiar with the install. They are quite involved with a lot of drilling and passge plugging, it has to be done a certain way, and the instructions frankly suck at being intuitive and neatly layed out. Superior makes a shift kit that is a lot easier to do, much less intrusive, and can be reversed. A TransGo cannot be reversed after install because of its complexity. Works really good but it is a 1 shot deal with no return flight.