I have to say your analogy is very good, because in essence, to prove Christianity is at least viable, you have GOT to prove the Gospels as historically sound, not as inspired, per se.
Once you prove them historically sound, you must deal with the question: WHO WAS THIS MAN? If you come to believe He is God, then you can see that He established a Church (we have not yet established anythign as inpsired). You then look to se what Church today would fit the description of His Church. Well, it has to be a Church that reaches BACK to His time, since He said it would never fail. It also, has to follow all His teachings and assume the structuce He said it would. The Catholic Church fits that bill. Then you see He promised the Church his guidance, and from THERE you can determine the infallibiltiy of the Gospels.
And once you believe in the Catholic Church, you do not really need historical evidence anymore. That is what LEADS you to the Church.