Someone here is thinking again with 1955 technology.
There are some pretty big reasons for not wanting to swap a 4 speed transmission for the 6 speed transmission, none of which has anything to do with saving money or gas mileage.
The problems you are going to run into, besides the fact that the transmissions are different and the transfer cases are different and the electronics’ are different and the wiring harnesses are different and the mechanicals are different is going to be the price.
The last 4L60E transmission I bought at the junk yard with supposedly 40,000 miles on it, cost me $500
The six speed transmission you are looking at is going to cost $1500
The problem is - it is just too new. There are not a lot of good used units out there to be able to just walk into a junk yard and give them $100 and come home with a good unit. It is going to cost you 4 times as much to take your old transmission out and put the new transmission in. Even then it probably won't work and you are going to have to spend another $1000 on top of that - just to try to upgrade your old vehicle into a newer vehicle.
The six speed transmission has not been out long enough for us to really know what is going to go wrong with it and what it's strong and weak points are. But you will not see any real improvement in gas mileage with that transmission.
The only difference between a 4 speed and a 6 speed is that the 6 speed has more forward gears in it. The final drive gear ratio is the same.
I actually don't see any advantage to the 6 speed, unless you wish to run faster gears, which is the reason they put the 6 speed in the truck in the first place. The lower first gear helps it to pull out. It just offsets the regular 3:73 final drive gear ratio and allows you to run 3:42 or 3:23 gears and yet the truck will still feel like as if it has the deeper gears in it.
The 6 speed transmission does not spend a lot of time in any one gear unless you are puttering around town. Even then, it hunts for the right gear all the time and when the engine starts to lug, it down shifts one or two gears and the engine roars and yet the vehicle is not moving much faster.
It is ok where you have the newer style engine that only runs on 4 cylinders at highway speeds, but for around town, there is no advantage.
Go to a rent a car place and rent a new Chevy Truck, Tahoe or a Avalanche for a weekend or for a week and see if you can feel that there is something of value there before you plan on spending thousands of dollars on something you really don't need.
My guess is, if you keep the fluids and filters changed on the automatic transmission you presently own, it will last as long as the vehicle. There is no expiration date on your old transmission and just because other people has had a problem with them in the past, doesn't mean that you will have a problem with yours.