Rob, I have a SuperCab so it has the suicide door back seat and my front seat is buckets with a center console for my seating config.
Our tires have approx the same overall height to them (my spare is a LT275/65/18 Goodyear Wrangler load range C) while my 20's are Bridgestone Duelers.
They all have the 9.75" rear ends, even the Max Payload ones.. It could be the actual axles themselves are different? The Max Payload have the 7 lug hubs on them, so that means they probably have different axles. My leaf springs are 3" wide and while there are only 3 leafs, they are pretty thick.
I do have the 3.73 gears and it's 'tow rating' is #11,300 with a #17,100 GCWR.. Same as the HD payload BTW.. ;)
Once I saw that the Max Tow had the higher GVWR and payload, that's all I looked at after that. I wouldn't even consider the regular tow package rigs anymore. I found mine on the dealers lot too. It was the only Max Tow they had on the lot that I saw. It was tucked in the back row on the "used" side of the lot, yet it was a new 2013?? They had several other new 2013's there too, but all where FX4's or STX's.
Hopefully, that second friction sway control will help your situation as well as fine tuning on the WD setup.
Mitch