So, let’s say Trump issues an EO that directs the USPS to stop delivering mail-in ballots (for states withholding voter lists to the Executive branch) 30 days prior to the election, when most states start sending out mail-in ballots.

Do we have to rely on a Trump-compliant SCOTUS to use the Purcell principle that Courts — especially federal courts — should be reluctant to change election rules in the period close to an election, because last-minute changes can confuse voters, strain election administrators, and undermine public confidence in the results, even if the change is otherwise legally justified?

No, you don't need to rely on them. The lower courts would certainly issue an injunction if the Administration does something that violates the Constitution (or federal statute, in that case) - and it's not going to reach the SCOTUS in 30 days.

Even if the SCOTUS says the states now have standing and this EO is invalid, the SCOTUS is feeding directly into election chaos and uncertainty, which is exactly what Trump wants.

Perhaps, but the President has the ability to create chaos and uncertainty. The courts won't - and can't - prevent him from doing that if he chooses. Again, an EO doesn't have any legally binding effect on parties other than members of the Executive Branch - and is not functionally much different than the President directing the Postmaster General to do something in a speech, or an interoffice memo, or orally at a cabinet meeting. You can't get injunctions against those things, for the most part, because they're not formal government action at that point.

This is frustrating for a lot of people, but the courts aren't in the business of issuing advisory opinions or giving guidance to the public on what they think the Constitution requires. Unless and until the government acts in a way that creates a discrete justiciable case or controversy, the courts don't yet have a role. That often allows uncertainty to linger, but that's what the standing jurisprudence has always fostered.