Re-Planet Formation
I've not seen any theory like the one you are looking for, and to be honest, I would not expect to see one either.
I assume that such a theory would have to assume that a gas giant is all gas, after all if it is to "change into a rocky planet", then it would not have had a solid core to begin with. As I understand it, gas giants have rocky cores which form when they are born from the gas/dust halo around a protostar. They are only gas giants because they are large enough, and hence exert sufficient gravity to hold onto their volatiles, helium, and hydrogen. So, I don't see the clear distinction between "rocky" or "gas" planets which your theory would require.
Furthermore, I don't thing the amount of material in the rings around the planets of our solar system is very much. For example, if the rings of Saturn were somehow compacted you would only have the equivalent of a small moon or asteroid. If this was incorporated into the core of Saturn it would still be a gas giant. After all, the act of adding to the rocky core does not remove any of the gas that gives the planet its designation.