...directly to the brass pump tube with the associated difficulty of getting a strong bond (due to such factors as the very different coefficients of thermal expansion of brass vs steel, lesser solder "wet-ability" of steel, etc.), what about soldering a large ID brass shroud on instead? The easy to solder brass shroud would then...
1. Establish a strong solder bond that would help support the breech and reinforce the tube.
2. Contain and support the (maybe even swappable for multiple calibers) barrel.
3. Perhaps be enough longer than the barrel to hold a few baffles in front of the muzzle and so do that voodoo that they (baffeled shrouds) do so well.