I've always been under the impression Spock Prime is basically stuck in the new timeline. It is also a brand new timeline/universe that exists on its own. It didn't displace or change any other timeline. Nothing is "wrong" or out of place because of its existence. So, there is no need for a reset button because there's nothing to reset.
As far as Spock Prime trying to communicate with his Prime universe goes, why would he want to? To what end? To let them know he's OK? Why would that matter in the grand scheme of things? For what purpose would he need to go back even if it were possible to any degree? He's perfectly fine where he is.