No, you really are not going to need something that brings the boost in low RPM's. The shift lever is good at keeping RPM's where the system needs them

Seeing as there is no mention of rock-crawling, low RPM torque is not a factor here.
And, No, it really is not entirely as simple as plop a turbo + tune and go. But, it is possible to do the upgrades in steps that are more budget friendly.
Power to pull up a grade and ability to do so are two different things.
With the Burb's configuration, I had plenty of power. The cooling stack needed more help so I had to cut the speed and was one of those over in the right lane with the semi's that crawled up the 6% grade when I had the RV in tow.
Unloaded, the Burb would fly up the same grade and rarely drop out of OD (when it still had the slushbox).
Point here is that no matter which turbo, if you want to maintain highway speed up grades for any distance, the overhaul needs a holistic approach and not simply picking one component.
In the end, each of the turbo's is known to make about the same power, so it is just a matter of what else needs to happen around the turbo.
Toward controlling RPM's and managing the ATT's desire for 2K RPM's, this is really not a big deal as that is what the shift lever is for

You are way smarter than this generation of PCM, so driving the truck does call for a little more operator involvement to stay ahead of road conditions. Especially while towing.
One thing that will make a bigger difference than a turbo is the tranny. Ditching the slushbox was the best thing that happened to the Burb. Seeing as you are already planning to pull the motor and tranny, now is a good time to consider a swap.
Yes, a tune now will definitely make a difference as the tuner can lock the TCC a lot more than what GM did. It is really tough to tell what GM had in mind with its logic. Some comment that it was for fuel economy, but leaving the TCC unlocked in all the situations that unlocks it actually does the opposite.