Tire size/gearing for Ram DRW

Either gear ratio will be just fine. Not sure what issues you'd expect from either. You could do what you're doing with a gas truck.
If you want the most "power" get the 4.1s. If you want slightly better mileage running empty and like to drive fast on the highway, get 3.42s.
I'd assume slightly better mileage but haven't compared directly.

I run a 255/80R17 (~33x9.5) on my 08 with 3.73s. I tow pretty heavy without the camper, usually around the 26k combined and it does that without issue.

With the camper, I find that if I lock out 6th gear I gain about 3mpg and my truck doesn't lug along. Would I run 4.10s if I had them? Absolutely.

I had a 2016 Ram 3500 SRW crew cab long bed 4x4 Cummins Aisin with 3.42, only ratio available. The only issue I had was that I would lock out high gear in hilly country pulling the 5th wheel. I replaced that with a 2018 DRW equiped the same except for 3.73 rear gears. I can't tell much difference. I don't think I would get 4.10.

Love our Laramie. We have a ~6000 pound camper and flat tow a Wrangler Unlimited. No issues with power in the hills. Stock aluminum wheels and tires size.

I order my 2017 F350 dually specifically with 3.55 gearing as that was the lowest number Ford would build.
Still would not mind overdrive gear as with this gearing the trucks pulls up to 10,000 lb cargo on all grades between San Francisco and Las Vegas without dropping from 6th gear.
And the route has some nasty grades.

Considering the .64 overdrive, I really think that 4.10 is probably a better choice. My truck is a 2005. Only 3.73 was offered with the .79:1 OD mine has. In other words, mine screams going down the road compared to yours. Even so, I have to downshift on the really steep stuff. With a .64:1 overdrive, even the 4.10s will purr going down the road and it'll pull harder in every gear.

Putting wide tires on a dually, especially in the rear, is challenging. You can only space them out so far before you bust the max legal width. If I had a dually, I'd probably stick to tires in the rear that are near the stock width and only go wider on the front if I thought that was necessary for whatever reason.

I generally like lower gears. In my 05, I wouldn't have gone lower than 3.73 if offered, but if I had another overdrive, I would be thrilled to have the increased pulling power the 4.10s would give. Unfortunately my prayers for a 7 or 8 speed manual in a pickup have not been answered.

I had a 2015 Tradesman aisin with 4:10 and now a 2018 Larame with 3:73.
both with aisin only difference was the 2018 is 2wd.

The 3:73 does run around 500 RPM slower. TO be honest the 3:73 might help 1-2 mpg at highway speeds as we are moving a lot of air with the camper on. But even towing 7/14 box trailer without camper, I did not see that much MPG improvement over the 4:10. Now the 3:42 might be a little low for running highways with even just camper loaded, but worse case you might need to lockout 6th gear if the truck keeps shifting on hilly ground at highway speeds.

I think the 4:10 will have the advantage in the engine braking dept as I recall it would work all the way down to around 25mph.

But you said adding bigger tires: remember you need to get those tires between the truck camper jacks to load it (I live in central FL where I see these ridicules pickups with tires sticking 6" out past the fender edges).
I would picture bigger means taller tires, go with the 4:10. taller tires affect the gear ratio and the 3:42 may be too low.

But between the tradesman and Laramie, I would go with Laramie. I have the bucket seat option and I love those electric adjustable, cooled leather seats :) The other options are also great.
I think they will both hold trade value, but Laramie will have better trade value (but it cost more up front)

Kohldad, Did you try running in 5th gear, 5th in the 3:42 is the same as 6th with the 4:10.
The tire diameter affects the ratio and I would get an aftermarket wheel with the appropriate offset to alleviate any issues with the tires being too close together to cause rubbing.

Diameter is NOT your issue, it is width with a DRW, you don't want the two tires too close to each other as you will be getting greater heat build up between the tires, and stuff getting caught between them.

If you're not towing big heavy numbers then pass on the 4.10 gears.
Fuel mileage alone would make a big difference over time.