This is absolutely doable, and is really the logic behind most current physical election security procedures. Procedures are designed less to prevent tampering than to make tampering obvious. Re-voting can theoretically be done, because (public, real-time) records are kept of who voted at a particular polling place, not counting provisional ballots - look outside for a "street index" at your polling place.

(Source: am volunteering for the second time working the physical polls.)

I'd guess that repeating a vote favours whichever party has a particular demographic (younger?, less employed??) or whichever is better funded (to encourage/assist getting to polls) that subsequent votes get less and less attendees?

So, forcing a revote might be a way to swing a marginal seat in your favour.

As far as I know, elections can't be redone on a federal level. I could be wrong, but I certainly don't know of any situations where they have been.

They absolutely can be: see https://www.archives.gov/federal-register/electoral-college/..., specifically the section of the US code that speaks to "Failure to make choice on prescribed day" and "Determination of controversy as to appointment of electors". Basically - if for any reason a state can't pick electors on election day, it can do so afterwards by whatever (constitutional) method it desires; and if there's a disputed election and a state has a (pre-election) law enacted for deciding controversies that law just has to come to a decision within 6 days before the electors meet.