The diam of 12 ga chamber is .798, 16 ga chamber is .685. Wall thickness of a 16 ga insert would be 0.0565".
Hoop stress controls, so stress = Press * Mean Diam/2 wall thickness.
Assume 20,000 psi peak pressure, mean Diam = 0.7435". This puts peaks stress in insert, if entirely unsupported,
at 131Ksi. That is entirely doable with a heat treated alloy steel liner. If you use the readily available, and
easy to machine 4140, heat treat by oil quench from 1550F, then 800F temper, you get yield stress at 195ksi, which
gives a ~50% stress margin. Ultimate stress is 210Ksi. Temper at 700F gives yield of 212Ksi, ultimate 230Ksi.
Yield would actually just tend to lock the liner in place, not a bad thing, just considering worst case failure mode
behavior. Would not happen.
The liners would be quite light, adding relatively little to the weight. Might epoxy them in place to prevent some
future person from harming themselves if they didn't understand. Exterior original barrels, if epoxied, would actually
provide massive reinforcement, creating huge safety factor. Inner liner would guarantee no local failure if there is a weak
spot.
OTOH, making a .0565 thick liner might be a challenge on the lathe. Deep boring would need a long drill and reamer,
large size. Perhaps a piece of 4130 chrome moly seamless aircraft tubing would be a more reasonable starting point. 4130 will
heat treat to about 160Ksi, but with only 30 points of carbon will not get quite as high yields as 4140. But having relatively
cheap seamless tubing as a starting point may be the controlling factor.
Talk to the machinist Keith, if the engineer Keith thinks it might work.
Bill