Hello, I am happy to assist you today.
I used to work for a lot of these large banks as their foreclosure attorney, and I can't even tell you how common it is for escrow accounts to mess up the accounting of a mortgage at no fault of the borrower. This is not your fault and can be worked out, but will take some patience and determination.
First, you should send another letter asking for a full accounting of your account. Under the Fair Debt Collection Practices Act the bank must respond to you in writing with that accounting within 30 days. I would try to get this letter to go to the bank's attorney, either their legal department nor their outside legal counsel. That is your best shot to get it treated seriously.
I agree with your suspicions, and expect that when you see the full accounting you will see something went wrong with the escrow account.
Unfortunately, the way most of these loans are written, they can consider your loan to be in default if the escrow is in default, and they can also reject your payments if they are not payments in full according to their calculation. I know, sounds crazy. There is much room for improvement here.
The basis that they use to increase the escrow is laid out in your mortgage document, so you will have to look at that specifically. That can differ.
Let me know if I thoroughly answered your questions.