Is your scenario possible? Hell, anything is possible, but using your Ron Paul/BIll Richardson example, it is highly unlikely that you could get folks like that to abandon their basic policies and principles and agree on a consensus platform that may attract some disenchanted voters but would just as likely alienate their original core supporters.
BTW, there is such a movement,
Unity08, but it has gained little traction and is still just a blip on the fringe of the national political radar.
And if they were to win, how do they govern with a Democratic (or Republican) Congress that has its own policy priorities and agenda?
No, the only way to build a third party is from the ground up, not from the top down. It requires more than a one-time presidential/vice presidential "unity ticket". And that takes time...a long time.
The Green Party is probably the best recent example of how to build a third party movement. The Greens have focused on getting candidates in local/state elections first and have been marginally successful in a few states where they have won seats on city councils and state legislatures . Then build on that with candidates for national offices. Yet after 12+ years, they havent come close to having a viable Congressional candidate anywhere and even with a name like Nader as their presidential figurehead candidate in 2000, that did not advance the party as a viable option.
There are reasons why third parties have not been successful in the US. It requires long term commitments and organization beyond the initial feeling of disenfranchisement and frustration with the D and R parties and that is extremely difficult to achieve and maintain, paticularly since the D and R parties make the rules.
I still believe the best way forward to achieving your goals it to work within the major party that most closely shares your goals (even if they have drifted from those goals in recent years) and use the existing structure to move the party forward in that direction.
That is no easy task either, but it is the method I will continue to pursue with the belief that it provides the best opportunity to have an impact on national programs and policies.