Something does not make sense here. Your monthly payment (or biweekly, or whatever) can indeed only be prepaid (ie, paying November's payment in September, or whatever) until the new escrow amount is calculated.
But that's not a problem, because if what you care about is paying down the loan, you actually want to be paying *the principal in advance but not the escrow*. Imagine, for a moment, that you could keep making prepayments - your escrow balance would grow enormously, and that money would simply be sitting in the account, gaining zero interest, while your mortgage balance would be higher by the same amount, on which you *pay* interest.
In effect, you would be giving the bank an interest free loan, while paying off your mortgage more slowly. Really not a good move. Pay your extra principal and do your happy dance, assuming that paying down the loan is your main goal here.
-W