super6

I have a 2009 with a 5.3l, 6speed, 4x4, 3.42 rear end. It came with the Z71 package and has the 18" wheels. I have been having problems with the transmission and I am wondering if anyone else has experience similar problems. 45k miles.
Here is what happens.
When I pull away from a stop, it shifts very, very quickly (under normal driving, when I hammer on it, this doesn't happen) down into 2nd and third gear...it goes to 2nd before I even make it through the light. So, when I want to then bring it up to speed, it is already locked down into usually 3rd and wants to stay there unless I go past probably 3/4 throttle, at which point it jumps down violently to what feels like 1st. Seems like it is tuned very, very aggressively for mileage. Very, very annoying as it does that all the time..so neighborhood/slow speed city driving really stinks. Tranny is very confused. If I put it into tow/haul, it stays in gear much longer and there is no issue. Seems like it might be tuned for an engine with much more torque or a 3.73 or 4.10 rear end.

2nd. When slightly rolling (1mph or less) and then trying to accelerate, there is a slight 1/2 second delay, then the power kicks in and everyone's head jerks back. I have to be very, very, very gently on the pedal and feather it through this until the engine/power engages. This seems like it might be a throttle issue or something to do with the fuel delivery. Does this truck have a throttle cable, or is it electronic?

3rd. Problem. Towing. Under hard acceleration (not w.o.t., but well past 3/4 throttle) and towing 2k--4K trailer, there are multiple times where the tranny "jumps" or slips in between 2nd-3, 3-4, and 4-5. Engine revs slightly and it jerks into gear. Again...seems confused.

I have had this truck to the dealer for warranty work on tranny. There are no codes. They could find nothing. I explained everything to my dealer as I have in this post. It is due to go in again. I checked tsb's and couldn't find any that seemed to be related to the issues I am having. HELP