Whether or not he will be "found eligible" is a decision that you are going to have to make for yourself. Don't expect any Court to make that decision, because I would be willing to bet my life that no court will take it up.
The decision is not going to be made by the Supreme Court. This is a decision you are going to have to make yourself. Nobody else is going to make it for you.
The party? The party is in the bag for whomever represents the best path for a return to power, of that I have no further delusion remaining. There may be a state to take up the matter, there may not be. The electorate has become a herd of cattle, collectively speaking. The Electoral College is well on the way to ceremonial status in practice. The Congress certified Obama with no objections, despite his being a complete cipher with little in the way of a discernible paper trail, despite well-known and highly publicized doubts.
Any day in court will happen at the hands of a state, imho.