I think the 2 month escrow is contractual and in your documents. Usually the bank just increases your payment to build the buffer back up. Your prior provider may not have enforced it -I actually had a negative escrow balance once before I got the nice letter telling me the amount is going up.
If you're below 80% LTV, you may be able to call them up and just drop the escrow.
Also, remember the purpose of that buffer. If you don't pay, the property taxes and insurance is still due and it would take them 60-90 days to foreclose. You get the buffer back once you payoff the house.