I do have autopay, but that means I have to either (1) keep a bunch of money in a checking/savings account making 0.1% interest or (2) keep it somewhere with a higher yield but transfer it a bank account all the time.

I want to make a large payment now, reduce the amount of principle I am paying 3.75% on, and not have to worry about the mortgage in the slights for a year or three.

Now that I think about it, both my car loan and student loan worked this way.

As for principle/interest, if I paid an extra $20,000, it would be counted as an extra principle payment, and interest would accrue as normal on the lower balance. The new payment date would be based on when my growing loan balance, absent any further payment, would equal the balance if I had made regular minimum payments. A double payment would only delay the next payment by one month, but a 20x payment would cut the principle enough that the loan balance would take about 22 months to get back to the balance on the amortization schedule.