[Lynn Eades]

That may well be the case, however the production of a cast iron ring, followed by the machining, fitting, and finish machining, to end up up with a somewhat weak result just wouldn't be worth it. Especially in this day and age, where questions would be asked, if a failure happened.
To go to the trouble of casting the repair ring, you may as well cast a complete drum.
Another avenue could be to turn the outside of the drum, and shrink on a steel "support" ring, which would be safer. This would allow a greater bore size to the drum. I dont think you'll want to do this either.

Kevin, turning out the drums and fitting thicker than std. linings is common. Modern drum brake vehicles have a maximum oversize. Back when the carriers were in wartime service, you replaced with a standard part. Your drum has a strengthening rib on the outside.
What you need to do is ascertain the original diameter, and compare that with what O.S.your drums will clean up at. From there is the hard part. Is that O.S. acceptable from a safety point of veiw? (I dont know who you ask)
Once that's decided, then the rest is easy. An O.S. brake will work better than a std. one. (bigger effective dia., and bigger surface area)
You will need to fit the o.s. linings, and have them ground to fit exactly, the drum radius.
In theory both sides should be done the same size to ballance the brakes, however, I dont think you could tell the difference. It is probably better to take the minimum out of each one, as it might still give you room for doing it all again later.
I wouldn't put shims behind the linings. Every separate piece (including sleeves in, and rings on the drum) is a barrier, or potential barrier to heat transfer.(the faster this can happen, the more efficient is your brake)
Some of the heat from your linings is disapated out through the shoes. A thicker lining of one piece is as good as it gets. Bonding is good as it does away with the rivets, which would be the biggest single reason for having to turn out the drums.