Paul's play is designed to wrap up the Millenial vote. The recent barrage of annoying position statements from him -- GOP is too white, abortion isn't important, gay marriage isn't a big deal, voter fraud isn't a factor, illegal immigrants are a benefit, etc. -- are all designed to appeal to the "youth vote".
And they won't run away his father's supporters.
Given that bloc of voters -- which superficially promises to expand the GOP voting base -- he can perhaps parlay his faction into a VP nomination.
The speculation of Rand Paul as a veep for the rinos, goes back to when Ron Paul was being mysteriously soft on Mitt Romney, during the 2012 primary.
Rand Paul endorsed and campaigned for Mitt Romney, and now, as you pointed out, he seems to be campaigning for at least, the veep slot.