I must agree with LT that each district would be unique regarding whether or not a new party would be prudent or using Ron Paul tactics would be the best course.
JB suggests a new party, while using R infrastructure where prudent. This would allow the new party to begin getting traction where it is able, and R's elected on our platform to slowly migrate as warranted to the new party in their respective districts.
This dovetails nicely with LT, above as well as with Quiet Man's suggestions (see comments).
For the sake of discussion, let's assume a new Party is part of a good strategic move (in addition to using existing R infrastructure where applicable).
Extending our political contemplations - what would you suggest as a name for a third party?
Remember your target audience. Remember the rules of marketing. Remember to convey your intent in as few syllables as possible.
Most of all - consider how your enemies would spin it.
"The Jefferson Party" would, for instance, be murdered in the crib because of the slavery paint brush.
"1791 Party" would work for many of us - but we know the relevance of 1791 in a glance, and the overwhelming majority of people in the voter pool would have no clue.
"Rightful Liberty Party" works for me - everyone likes the notion of Liberty, the "Rightful" part can be explained with the Jefferson quote...
There is no avoiding the reality that political enemies will immediately try to link any new such party with slavery, given the language that exists in the USC, and despite the intent of that language. Any party arguing for a 'return to founding principles' will immediately be hit with Slavery and Women's Rights as issues. Personally, I'd answer such claims as I do on our blogs: Those considerations are disingenuous, at best. Every State in America has laws against slavery and discrimination.
But the smears will work, to a degree, for the malevolent and the un-thinking Souls. But, they aren't really the target audience, anyway.