Why not require anyone who runs for a federal office submit the same job application that those who need security clearance have to submit.
That's tempting, but it puts the government in charge of deciding who can run for office and creates the probability of the party in power using the check to kill any candidate by manufacturing a security breach problem. The Knights of Columbus could suddenly be discovered to be a subversive group.
You can’t make access to the ballot difficult. Frankly, a homeless person should be able to run for the Senate if they so desire as long as they are qualified.
I’m not sure making it more difficult to run for office is the solution to any problem.