The missing link was to a Federal government site about the procedures for paying money people running for president, including in the primaries. For some reason the lik doesn't work.

The point is, it's not a question of anybody barring him from election, it's about getting a court to confirm that by his own actions he has already done that to himself. It wouldn't need to be the government to launch a legal challenge. Whether the court would confirm that is an open question - but. I don't thank that any of the people he shoehorned into office would be likely to be affected by some sense of loyalty or gratitude in making their ruling.