I don't think you will see as much positive effect from the 3" sq. tube steel sides as you expect. For one thing, three inches is too big of a space. Two inches would be more apropriate. Do you have a bunch of tube steel in stock already? Tube steel is very expensive. Furthermore, it will take a ton of welding to make it that way. If I were totaly stuck on using that method, I would use something like 2"x 10" rectangular tube steel instead, and eliminate the majority of the welding. If this were my project, however, I wouldn't use tube steel at all, but rather I would use boiler plate for the entire construction and then make air passages where I want them, using just some 14 gauge steel.
As to the double bend, this is just not a good idea. What you want in ANY piping system, but especialy a stove flue is no bends, or as absolutely few bends as possible. If it were me, I would change the design enough to allow the vent to leave the top of the stove instead of the front. It could still exit from the front part of the top though, still giving you the full benefit of the smoke shelf. Good luck, and keep posting.