I have a 2003 2500hd with 4.10's and a 4l80e trans (4 speed). They don't begin to produce any power until they are above 3000 RPM.
When climbing the transmission has a tendency to upshift - about 300-400rpms when I want the RPM's around 3000. I find if I take my foot off the throttle and then step back down, it overrides the half shift (as I call it) and then stops hunting. It also puts me back in control of the RPM's around 3000+.
I've asked on other forums but nobody seems to know how GM has the transmissions electronic rules tied to it.
Maybe someone on here knows.
I put a 16 pass stacked plate, electric fan assisted cooler on the transmission - and per lawrosa - I should be above 175 climbing; However, On a long hill climb I generally will end up with about 200-220 for trans temps.
Don't flush your transmission!!!
Have your mechanic drop the trans pan cold, then clean it and replace the filter. Then you can have the remaining 10 quarts swapped through a flush.
Most of the time,the flush will stir up the particulate matter inside the transmission and wear things out prematurely. It's more expensive, but worth it (or you could do it yourself).
I do this annually generally after I do the trips (that way if something does get into the transmission, I don't find out about it on the road).
I've got over 160k on my Trans towing and it's in good shape.