If you asked any Founding Father, supporting the legalisation of gay sex, let alone gay marriage, would be unacceptable to the same extent that legalising genocide would be to us. It's like incest is to many nowadays- just instinctively disgusting. They would consider themselves morally against homosexual behaviour on principle. It follows that if you claim to be acting "in the spirit of the Founding Fathers", you cannot support gay marriage without hypocrisy.
The Founding Father's concept of common sense and ours are close enough we can extrapolate. For transport, for example, how on earth can a flying machine NOT be transport? Just as a teleportation network would clearly be transport, and we know that even though we don't have them.
You can talk about the principles on which the nation was founded, one of which was very clearly that blacks and whites are not equal (yes this was amended, but not by constitutional means). But that isn't the same as the principles of the Founding Fathers, nor the tradition of the Founding Fathers.
If you said the values written into the Consitution, which means something quite different, on the other hand, I would agree with your interpretation mostly. My point on race still applies, and forcing churches to perform marriages would clearly violate it.