They have the final say on constitutional matters, so I believe they can and will, sadly.
I would think even a strictly non-partisan court would be likely to hold, following
United Public Workers v. Mitchell, that Article II trumps the Tenth and Fourteenth Amendments. Letting state courts make that call in a national election opens a sizable can of worms with respect to other landmark decisions and legislation.
The easiest hole for the Court to swim through is the fact that the presidency isn't enumerated in Section 3 of the Fourteenth Amendment. It's an oversight, because the authors were planning around the aftermath of the Civil War and couldn't conceive of a former Confederate officer or official being a viable candidate for the presidency or vice-presidency. The dissenters will be likely to point this out. However, it gets the majority out of Dodge without having to revisit precedent, and in a way that doesn't create precedent for other legal issues.
It's the cleanest way for the Court to make the problem go away in a manner that doesn't affect the agendas of the various justices, and that might get better than a 6-3 partisan vote. Roberts will want that result if at all possible.
If McConnel and other GOP senators had done their duty rather than play political games they would have convicted Trump for impeachment for Jan 6th and he wouldn't have been able to run in 2024.
Impeachment has become a political tool, and nothing more. The days of senators like Howard Baker are long past.
The big question is what happens when everything is out on the table. Should Jack Smith secure a conviction on the classified documents case after the non-MAGA crowd sees how bad that one is, the game may change. There really isn't any telling.