Since you're escrowing your taxes with your mortgage company, here's an advance warning: when they pay the taxes on your behalf next time around, there will almost certainly be a shortage, and they'll likely send you a seriously-worded letter to the effect that you can either send them a check for thousands of dollars to cover it, OR they will jack your payment up sharply for a year to make up the difference.
The wording is usually chosen to sound like a threat - "Pay us up front, or you'll be paying us more for a year!!!"
RUN THE NUMBERS - once you see how much they want to jack up your payment to cover the "shortage" you'll probably discover that over one year, the mortgage company's "extra" charges exactly equal the "shortage" payment they'd like.
If that's the case, only a FOOL would send them a big check up front - because by paying a higher payment over the course of a year, you're essentially taking advantage of an interest free loan with a one-year term.
Like I said, run the numbers for yourself.