I ran the numbers several ways...chamber pressure, and vibrations.
Pressure-wise; both the hoop stress on the reduced chamber diameter, and the axial stress on the welds are well below what the material will hold (even with the weakest of steels and a fairly high design factor).
Vibration-wise; as a dynamic/shock loaded cantilever made from a non-brittle material with a stress concentration at the chamber/thread shoulder it is also well within any forces it will see. It would take someone jumping on the end of the barrel with the action in a vice to do any damage. Surprisingly, both the shear and bending moment diagrams are fairly linear without even taking into account the barrel shoulder that's contacting the action.
I understand the concern and will certainly keep a close eye on the barrel, but it should be amply strong to handle all forces it will see.