I would say yes you would see an improvement with dual 2 1/4 vs dual 2 inch. Have you ever considered hedders? Hedders with dual 2 1/4 on a 340 would be perfect in my opinion, and I also think that your idea to have an h pipe (crossover) is another good idea.
I have a 300hp crate 360 magnum and I put it in a 1991 dodge power ram 150 4x4 truck, The previous owner had just gotten new dual exhaust for the 318 that was previously in the truck and he got dual 2 inch pipe, I hooked up my hedders to this dual 2 inch exhaust and ran it that way for about a year. Then when I had the money I took it to an exhaust shop and I had them re-do the exhaust with 2 1/4 pipe. I had new dual 2 1/4 inch exhaust put on along with an H pipe and then I had them put some 3 inch inside core diameter glass packs that are 18 inches long on for mufflers. When I drove the truck for the first time with the dual 2 1/4 inch exhaust I could tell a difference in power and sound, my torque seemed a little better off the line and it sounded more like a mopar too.