Tow/Haul does nothing for the shift points. Shifts identical to not having the button pushed... except 6th is locked out.
If it would shift at 2500 or so loaded that'd be good enough for most instances. There's been a couple times when it shifts at 1900 or so going uphill loaded. That's when it shakes and almost dies cause it can't pull the load. I'm going to the dealer tomorrow for my fuel tank (finally) so I plan on hitting them up about it.
Yours shifts entirely different than mine. I agree with HBarlow, something is not right with yours. Mine never drops back to such a low rpm that it shakes and almost dies, something is not right with yours.