Bush will not take out any ire with a new nominee. He knows he doesn't need the aggravation. But, I don't suspect he'll do much to advance them.
No, I think Bush will wait and pick another area of policy in which to differentiate himself from the fringers.
Bush is not going to allow himself to be a captive to any particular part of the GOP.
Reagan didn't do it, and Bush won't either.
But I think we can be sure that the names discussed here will not be on Bush's list.