Point of information: In 33 states + DC, laws require that the counting of votes be audited no matter what the results were. The remedy, if discrepancies are found in a sample audit, is usually a recount, though the scopes and types of those recounts vary. (Yay federalism.)
The hypothetical is interesting, though completely implausible (sorry). I think there are three broad categories of response that I’ll call “bureaucratic,” “political,” and "non-governmental." These names are probably lazy and bad, but here’s what I mean…
By “bureaucratic” I mean actions taken by government officials under whose purview potential election-related crimes would fall: secretaries of state, registrars of voters, various law enforcement agencies, and the like. I would absolutely expect investigations by many of those officials and agencies in this scenario; they already investigate allegations of election crime – most of which come to naught, but it’s their job, so they do it.
But legislators at all levels (yay federalism) have the power to conduct investigations, and in these cases it’s going to be a political question, resolved politically, based on the balance of power within each chamber of Congress/state leg/county board/whatever. And, of course, on the specific character/situation/ambition of every legislator who gets to vote on whether to investigate.
I would expect that in the OP’s hypothetical, relatively few elected Republicans would sign on to investigations – sorry, Republican fans, but recent behavior by your legislators makes this a safe inference, IMHO.
Swap the parties, and I’m much less sure about what would happen; “count every vote, even if we lose thereby” has been Democratic rhetoric in contested elections since at least 2000, and I imagine there would be intra- and extra-party pressure to hold them to that. Would that pressure work? Are Democratic legislators more likely to stick to principle before party?
- And of course we have non-governmental institutions that would investigate the election. Media organizations, natch. Also various think tanks and public advocacy groups. The goo-goos (good-government types).
One last point: basically, all of the solutions to any finding of malfeasance in this situation are political – right? Here are some I can think of, details varying by state (yay federalism):
- state legislatures overriding vote counts
- pressure on EC electors to be faithless
- Congress refusing to ratify EC results, taking election to House/Senate
- post-inauguration, impeachment and removal.
The lack of an apolitical solution ultimately means that all investigations are highly prone to politicization. For this reason, the chances of developing a fact-based, bipartisan consensus on what, if anything, went wrong would, IMHO, be pretty low.