Gassers and diesels need different gear reduction.
A Duramax/Allison combo runs and overal gear of 14:31:1 in 3rd gear low range or 10.15: in hero gear (4th gear) low range assuming stock 3.73 rear-end ratio. I ran 33's locked with roughly 500RWHP and could not run 4th (stayed in 3rd). I started in first and let it shift to third.
Whereas:
With my gasser I run a custom TH400 first gear planetary of 3:1, a NP205 with 1.96:1 low range, and 4.56 ring and pinions locked with 35's and run 550RWHP with a lot less torque than the Duramax. I start out in first gear and DON'T shift and sometimes wish I was geared a little deeper.
With a 33-35" tire most guys like to be in the 28:1 to 30:1 final drive ratio. With 37's you may want to try a little deeper 32ish if your gearing allows it.
I know from talking to guys running the 203/205 doubler that running the high side of one of the cases is not a good idea for high torque (it may be the 203 but would have to research it), but may not be an issue if you have both cases in low.
Running that short a wheelbase is going to be a little tough (especially with those tires), but if your just trying to see what it can do...go for it. Definitely weigh up to max limit. Set your hitch at max height for now, but thinking a few inches down might not be a bad thing (won't know until you actually pull) as those tires and short wheelbase will want to lift the front (sometimes a lower hitch can help combat that to a point...but it's a give and take).
Doing the math with 4.56 R&P and TH350 gears of 2.52:1, 1.52:1, and 1:1 the closest gear I can find is with the tranny in 2nd with both t-cases in low for 26.62:1 reduction. That would be pretty good with a torquey motor and 33's locked, but with 37's it is marginal. Only one way to tell though.
Let us know how it goes.