So, let’s say a political party is somehow at fault for charging and getting a verdict of an opponent. This would make it very easy to block anyone from running against the party in power if they so choose.

The founding fathers saw how much of an issue this would be so limited the reasons for blocking someone from running for office. I don’t think hush money is a good reason (though, doing so to block info that would make him lose an election I think should be but that will be up to the court)