Good grief, you *are* naive, aren't you?
Replaced by whom, another state chair whose jib is cut the exact same way. State party politics are almost always driven by personality more than ideology, except in very rare circumstances where a determined ideological minority raises enough of a ruckus that the rank and file wakes up for a moment and gets mad enough to turn out in force at county conventions.
Most of the time, however, when one state chair (or other top official) is replaced, it has to do with factional politics - one guy's circle of followers was able to finagle a way to get the other guy thrown out.
No, by whomever you are postulating for the same position in your third party. If you don't have such a person, or the person is not a good one, or you cannot organize for, nominate and elect such a person...
Then you just can't do politics on that scale. You can't do it on a large scale in your third party either. IF you can, you can do it in the GOP, easier.
I agree it would be much easier to have a house party and all agree on each other for the key positions. But then what?