There is no paperwork to be "submitted". All the paperwork stays with the store until they go out of business or lose their FFL. You will not get a letter from the DOJ because the DOJ won't know anything about it until/unless there is a BATF audit. At that point, the BATF (depending on the severity of the problem) may hassle/fine/threaten to fine the store but you as the buyer are home free unless you put down conflicting information--i.e. obviously lied on the form. Even then the store is in as much (or more) trouble as you are.
The next time they call, tell them to quit BS'ing you, that you know the law. Then explain your situation and tell them that you're willing to work with them to get this solved, but not if the entire penalty (a 4hr, 200 mile round trip) is going to be borne by you.