Not nitpicking, they were never classified as a firearm, it is considered an NFA item. Therefore requiring a federal tax stamp. NFA being a law enacted in 1934.
The BATFE never really handles your payment, make no mistake, the money is theirs, but opening the envelope and cashing the checks is outsourced to a bank as far as I know. Then the forms are transferred to the BATFE and supposedly filed in order of receipt.
EDIT: My last 2 submissions, one a form 4, one a form 1(SBR) were mailed to separate addresses, approved one day apart by the same examiner. We all have our beefs with them, and no they are not going to miss lunch or work even 1 minute of overtime to approve you, but they are somewhat efficient, cough, cough. Most approvals fall into time frames associated with work load, and if one of yours was delayed for extended times, it was most likely in background checks because some clown with the same name somewhere is a dirt bag, lol