Spring-over axle conversions on trailers are common and I don't think that the difference in center of gravity is enough to warrant concern for a competent driver.
The only real issue is the increased overall height of a big Fiver, many of which are already 13'6" with A/C and satellite dishes and such.
Fifth wheel manufacturers have offerings with more bedrail clearance. Go test some.
The effective gearing change from the 37" tires would be the biggest detriment to towing. Those 37" tire actually have a higher load capacity than the stock tires -123 class vs. 121- and as long as the wheels are from a reputable manufacturer I don't see an issue.
I have literally millions of miles of towing experience, many of which involve piloting a rig with a 90' overall length and a 14' height.
My advice would or OP? These options:
1: Test-hook different 5th wheel offerings to judge clearance. You might find one that works.
2: Do a spring over axle conversion if your preferred 5th wheel does not offer enough bed rail clearance, provided the overall height doesn't exceed 13'6". Even at 13'6" you need to pay attention to overhead clearance.
For either option, the stock gearing may not be adequate to pull a large fiver. A 4.10 might be borderline. There's a difference of tons in towing capacity rating within the spread of 3.55, 3.73, 4.10 and 4:30 gearing (or whatever the Dodge/RAM options are). Those 37" tires effectively give you taller gear ratio unless the truck was re-geared. If you find a set-up that works and the truck wasn't re-geared, re-gear it to get it to the 4.10 or 4:30 stock equivalent.
3: Buy a set of stock take-off wheels and tires for cheap off of Craigslist or FB marketplace and swap them on when towing. It'll give you a couple of inches of clearance and improve the effective gearing.
4: Change the Dually back to stock. It wouldn't be as expensive as you think, but it does defeat the purpose of buying the bro-dozer you like.