Great thread.
Just to add more real world experience, my old 96 burb, similar to your old one, never exceeded 200F trans temp pulling hills. It had the factory external trans cooler and the in radiator one in series. Same trailer as in my signature.
It would lock up in third, and OD, although when pulling it was always in 3rd. It would not hold OD at all with the factory 3.73 gears. My camper is very similar in weight to yours...slightly heavier when we are loaded up.
When going up hills, I would try to ride the converter as much as I could, keeping it locked while in third gear...however some hills required 2nd gear with my foot to the floor. No lockup there.
Our new suburban has a 4l80, which also locks up in 3rd. You have to be over a certain speed and under a certain % of throttle position for it to do so (just like the old 4l60).
I'm not 100% on the criteria for the gmt800 trucks, but I was under the impression that in tow/haul it would try to keep the converter locked longer. Forcing it into 3rd might not be needed, but it should not prevent the convertor from locking up.
If the computer was commanding lockup, and not getting it, you would get a check engine light.
I agree with everyone, you truck, with 4.10s and a 6.0, should have no issues with that camper. Sounds like an inspection of the cooling system is in order.
How big is your factory external cooler? I would service the transmission, after heating the fluid up like that a few times. Check that fan clutch too. It doesn't make sense since the engine stays cool, but installing and HD clutch in my old truck made a noticeable difference, even though the old one seemed good.
Love these suburbans, our old half ton was a great truck. But once we started doing long 2-3k trips and hitting steeper grades, I was worried about sending it to an earlier grave.
So we sold it and got our "new to us" 2500 burb like you did (I've always wanted a big block suburban), and unfortunately have to work out all the kinks we already addressed in the first truck. But I think it will be worth it in the end.
