1. Use a razor blade to cut the damaged ring(s) all the way around at the glue seams. Favor the good rings above and below the damaged one so that their edges remain intact.
2. Cut into the damage rings as need be to remove them. Pliers may help to gouge and twist them out.
3. Use a narrow band of sandpaper to remove any remants that adhere to the blank. Any that don't come off easily can stay there; you just need a good clean, reasonably round section for bonding to the new ring.
4. Ream the hole on a new ring to the approximate diameter of the exposed blank.
5, Using a razor blade, cut the ring in half across its bore.
6. Insert and fit the the halves onto the blank,making sure the cuts match up neatly, and checking that the bore is snug to the blank, sanding it a bit more if need be.
7. After checking fit, insert and glue the halves onto the blank and pressed together.
8. Once the glue is dry, hand sand to shape.

No harm in trying that, but the epoxy glue, flexing differently, expanding and contracting at a different rate, and being stronger than the substrate, may simply tear/break it again at a slightly different position. If the goal is just a cosmetic repair, a relatively weak, flexible adhesive mixed with cork dust will work better.

Yup, but same thing. No harm trying, wood glue fitting the bill. But according to the description, the ring/crack opens under flex. The cork is fatigued/dried and with less resilience than new cork because the flex has compressed it and it doesn't return to shape when the rod straightens. So reglued or not, quite likely it will do the same thing. A fresh, resilient cork ring probably will too, but only after a much longer service life. A new ring can be built up on its flats very slightly before installation by gluing on sheet cork, then sanding almost to the original flat. In this way, that slightly plumper ring has a bit more flex and cushion to prolong its life before it cracks. I like the idea of simplest first when it doesn't obviate another method, so if I were new to the process, I'd at least have the glue injected, maybe a little cork dust mixed in by now.

On the other hand, if the hesitance is the cutting and inserting, I'll just say it is so easy even I can do it, as could anyone else old enough to handle a razor blade. After sanding, and once the grip is uniformly clean/dirty again, such a repair is virtually undetectable.

Thanks all!

I have some fine tipped needles that should do the trick for injecting adhesive. I'm going to try a flexible adhesive first and see how it does, though I like the idea of cutting the cork out if I need to. That seems like a relatively simple fix if it comes to that.

Thanks again, I'll probably post again after I try the adhesive and get a day to test it out.

Nate