You could bend some thin, say 1/8" thick, white oak or ash to build a reinforcing ring or particial ring and glue it to the existing ring using a good water proof glue or IMHO epoxy. You can purchase some smaller containers of epoxy glues at you local hardware store if you do not have a current source. Try to stay away from the 5 minute types as I understand they are not as strong. A possible source for the wood - assuming you do not have any - are the rings used for embroitery. They are cheap and suitable for what you need. I think found this idea here.
I hope this is useful,
John VB