The good news doing that is that you replace what may be cast iron teeth with steel teeth, which are less likely to break.
The big issue with many such gears is whether there is enough meat on them to do the job. Some, such as the OP's, have the inside undercut for various reasons, and there is not a lot of rim to hold a ring after turning off the teeth plus enough more material to give some "base" to the new teeth.
The picture shows that there may be just barely enough to do the ring, but it will be really close. You need enough "base material" to stand the press fit. A snug "loctite fit" may be less dangerous, and with all that area, if the ring idea can fit, loctite should hold well..
The Rivett has a ring of index holes in the rim, and the rim is not thick. It may be possible to get a ring onto it without losing the index holes, but it will be close. I opted to replace it for that reason.
The thickness issue is why I like the braze and recut plan. Also, there are not that many teeth missing, so the ring is a bit of overkill, steel or not.
