@Jonathan *******
no way to avoid it, but also you'll need to be careful while on overstay. If you end up being checked by the police you can be arrested and deported for overstay, a bit of a nightmare if you don't have a valid passport. My passport is in the post isn't an excuse, if you don't think you're passport will be back in time I'd recommend leaving Thailand while still legal, even if that means returning to the US and starting over.
I question the "I'm now being told" statement, when you last applied for a 12 month extension of stay the stamp in your passport should only run until the expiry date of your passport