how long will it end up taking to actually go through the process
Until December 14. At that point they need to have Electors appointed, or else things get...weird.
...and if there be more than one who have such Majority, and have an equal Number of Votes, then the House of Representatives shall immediately chuse by Ballot one of them for President; and if no Person have a Majority, then from the five highest on the List the said House shall in like manner chuse the President. But in chusing the President, the Votes shall be taken by States, the Representation from each State having one Vote; A quorum for this Purpose shall consist of a Member or Members from two thirds of the States, and a Majority of all the States shall be necessary to a Choice.
tl;dr: If the states' Electors don't pick a clear majority, then it goes to the House. Each state's Representatives vote on what to do with the state's Electoral Votes.
Apparently this has only happened twice.
I think the Twelfth Amendment gives the House a shot at it first, and both of them go to the Senate if the House can't sort things out.
That's certainly not a bad idea, but how long will it end up taking to actually go through the process of Voter Mails Ballot -> Ballot Rejected -> Voter Notified and Mailed New Ballot? -> Voter Mails Second Ballot -> Count