I propose something unusual: Paul should invite Perry, Santorum, and Bachmann to a private debate, off the record, with no audience at all. They don't even need to tell anybody else about the debate.
Paul should state plainly that his purpose for inviting them is to convince them to endorse him after they drop out of the race. Give them as long as they need, even if it's an entire day, to grill him on all the issues. On some of them, Paul might be able to change their minds. On others, they might even change his. But if he can convince them that his positions, especially on FP, are tolerable, then surely they'd prefer to have him as president than either Romney or Gingrich. The possibility of getting their endorsements is worth the effort; their support in national polls, combined with Paul's, is slightly more than Romney's, and many supporters will follow the endorsements.

Paul should also ask Santorum and Bachmann to call him before they announce that they're dropping out of the race, so that rather than just dropping out, they can announce that they'll fill prominent positions in Paul's administration. In addition to helping to ensure that their supporters follow the endorsements, this solves Paul's serious lack of support from female voters, and the combination of Paul, Santorum, and Bachmann might be enough to sway a lot of values voters away from Gingrich.
Having a female VP candidate would also help mitigate the inevitable smears in the general election that only racists would vote against Obama, because the obvious retort would be that only sexists would vote against Paul's VP.