While the party has become an ineffectual weakling on the national level, it remains an effective force at the state level -- controlling thirty of the fifty states.
Let several of the more important state parties -- say, Texas, Wisconsin, South Carolina -- declare their independence from the national party. Then, see how quickly other state parties might follow suit.
The only states we need to concern ourselves with are the states that lean Republican at the national level. I.e., how the California Republican party reacts is of no consequence.
An intra-party insurrection at the state level is the best way to achieve reform of the national Republican party. There is no need of a third party if such an insurrection is successful.