Hard to say what Reagan would have done.
In 1976 while scrambling for delegates before the GOP convention, Reagan named as his running-mate-to-be Senator Richard Schweiker, the most liberal Republican in the Senate.
Oh, and in 1980 Reagan named as his running mate the well-known moderate Republican, George H. W. Bush.
I heard about that...Shhh!! You don't want to spoil anyone's hero-worship.