What is my recourse regarding a moving company's overcharges?

The issue is, what exactly *was* the agreement? If the quote was firm, they have to honor it. If it was a "good faith" quote, then it *may* be enforceable, to the extent that nothing changed between when they made the quote and when you actually had the move--for example, you did not add additional items or an extra garage or shed or storage room full of belongings. Also, you have to consider what the agreement or proposal or quote said--if it explicitly stated that it was not binding, it's clearly more difficult to enforce, unless you can actually show fraud (basically deliberate lies made to you to get you to give them your business). In short, you may have a breach of contract claim, but whether it will actually prove out depends on the circumstances and exactly what was agreed to.