NY23 is a perfect example. The third party, does not have much chance until it reaches a certain critical mass. Once it does, however, all bets are off and one or both of the incumbent parties may implode. This critical mass may be achieved when a significant number of high ranking elected officials switch to, or support the third party candidate.
Your answer makes sense to me. However, the state parties have so much control right now that in some states there could be major problems or roadblocks to get a viable third party on the ballot. Governors weild a lot of power and influence.
I would like to here a discussion on how we could get around these obstacles. I speak from some experience. When a group of Conservatives tried to take over the local Republican Party the Governor made it impossible for us to get control.