It's fairly obvious, you want to have a very capable offroad vehicle, that apparently requires overly large tires (38"+) to give it the capability you are after, and it should still be able to tow fine.
Can't happen unfortunately. You want reasoning......
1. (the biggest factor IMHO) do you not understand the difference in sidewall height? If you are going to use, say, a 16" rim, there will be a ton more sidewall with a 39" tire vs. a 35" tire. That will make the tire more "bouncy" since there is more rubber to absorb the force of a bump, and then release that energy back in the opposite direction, bouncing back. That is part of the reason towing tires generally are 65psi + because it makes the tire "harder" and doesn't give off as much bounce back.
2. If you go with a 38" swamper, it's probably at least a 14.50" tire, or wider. Wider doesn't equal to better towing control. When compared to a milder 35x12.50, you are going to have less side to side control as those wider sizes are going to catch more grooves in the road. Anyone that has ran wide oversized tires knows what I'm talking about on the side to side "grab" that we all have felt here and there. That only gets worse when you tow and have more weight on the rear and less on the front.
3. The taller the tire, the taller the truck. The taller the truck, the taller the drop hitch. The taller the drop hitch, the further the tongue of the trailer is from the strongest part of the towrig, the frame. This gives a trailer a certain amount of "leverage" against the truck. While it's really not the big of a factor, it is something to consider.
4. Pulling power. Having the drag of big a$$ tires is already like pulling around a small imaginary trailer to begin with, the more you add to that, the less power you'll have available, the more fuel you'll use, and the more your brakes will have to work to slow down the heavier inertia of those huge tires, along with now the trailer load that you are towing.
Can you tow with 38's? Yeah, but I wouldn't tow more than about 1500lbs, and forget bad weather towing and mountain passes. Moving down to a 10 ply 35x12.50, I wouldn't be afraid to tow as much as 3K.