Well I am going to have do a little surmising here. :h I tow a 10K ish fifth wheel with a 6.2 CC SB that has a 4.30 diffy. I was not in as time crunch like you so waiting 8 weeks for the truck to get here was not s problem.
This year I will be running 3 times thru the Smokies so will get some grunting time in like on the Saluda grade.
Personally I think you will be running mostly 5th gear. That may not a bad thing though. I have found that the 6.2 needs a few R's to make any ponies and it starts to bog in 6th anywhere under 2000 R's.
So I think you will get along OK with the 3.73 if you are not expecting to chug along in 6th and say cruise at 60 mph.
