I think they will rule that individual states can’t use the amendment to keep candidates off of primary ballots. That much is clear.

But the challenge isn’t that he’s not eligible to run in the primary. The challenge is that he’s not eligible to run for President. So if they rule that he isn’t, and they do it quickly, states will have to leave him off the ballot in September(ish) when early ballots are printed.

I wonder if they rule that Trump must remain on the ballot, but cannot serve if he wins – unless waived by Congress.

If he’s eligible to be on the ballot, he’s eligible to run for President. There’s no mechanism where SCOTUS can say “yes you can run, but we say you can’t be sworn in.” Their only opening is on the eligibility question, which is a simple yes or no.