You're making the same mistake as those who think the SC, or the EC decide the election. That's just not so.
Evidence of a fraudulent election will be judged by the Congress. It certainly has to be developed in courts to be persuasive! And it needs to be very persuasive.
But the judge and jurors of the electoral trials are the Congressmembers.
And their deadline is, I believe, Jan 6.
“If her case isn’t resolved by the time the EC votes, it’ll be dismissed as moot. “
That’s possible... but not necessarily the case.
It she proves the EC is improperly constituted... it ceases to be the EC... when a judge rules that it is not.
What you are discussing is not the requirements of law... but those of tradition, or custom... that presume no issue in law exists.
If “Russian interference” in the 2016 election was enough to remove Trump because of it, after the fact, in spite of his having been proven to have played no role in it ? That makes it clear enough that there IS NO DEADLINE re countering the impact of fraud in elections ? The one that does exist... as a practical matter... until you gin up the next round of impeachment trials... is the closure of process with the taking of office being allowed by a sufficient number to enable its legitimacy.
Assume a perfectly split vote... and two Presidents holding dueling inaugurations ? But, that can’t happen, right ?