The BFATE used to have a letter many years ago dealing with damaged/obliterated serial numbers on firearms and how they could be made acceptable.
I can't find that letter any more, but maybe someone else could. At any rate, the wording of the various laws has changed over the decades, and now it's different. That prior letter is worth less than the paper it was printed on.
The NFA, 26USC53, is quite explicit on the matter nowadays. Here's a link to it:
https://www.atf.gov/file/58141/download
Section 5842 Identification of firearms (starts on page 94 of the above link) says:
(a) the manufacturer shall identify each firearms by a serial number which may not be readily removed, obliterated, or altered, plus some additional stuff. If I were you in your circumstances, I'd have a beef with the manufacturer because your description of how FN affixes the serial number to their guns doesn't sound like it meets this criteria.
(b) If you possess a firearms which does not bear the serial number and other required information described in subsection (a), it shall be identified with a serial number assigned by teh Secretary and any other information the Secretary may prescribe by regulations.
One might read (b) above as meaning you can appeal to the Secretary to have a serial number assigned. HOWEVER, this may not be the case. Why?
For this we need to go to section 5861 Prohibited acts (starts on page 99):
It shall be unlawful for any person
(h) to receive or possess a firearm having the serial number or other identification required by this chapter obliterated, removed, changed, or altered; or obliterated, or
(i) to receive or possess a firearm which is not identified by a serial number as required by this chapter; or
(j) to transport, deliver, or receive any firearm in interstate commerce which has not been registered as required by this chapter; or
Right now, the way the NFA is written, your pistol is not legal for you to possess. Period.
This places you in a Catch-22 situation: You have a firearm in your possession which HAD a serial number but which NO LONGER DOES. This is illegal under the section 5861.
BUT...5842 seems to have a provision which allows you to identify the firearm with a serial number....but to do this you would first have to admit to the criminal act of possessing such a firearm in the first place.
Now, the NFA dealt with a specific class of firearms. But the GCA also supports this as well. It is illegal unde 18USC922 (k) to possess any firearm which has had the manufacturer's serial number removed, obliterated, or altered and has, at any tiem, been shipped or transported in interstate or foreign commerce.
https://www.pennlago.com/are-firearms-without-serial-numbers-illegal/
https://www.govinfo.gov/content/pkg/STATUTE-82/pdf/STATUTE-82-Pg1213-2.pdf
https://www.law.cornell.edu/uscode/text/18/922
NOW....WE CAN CALL THIS "UTTER NONSENSE" with respect to destroying the frame. HOWEVER, NONE OF US HERE ARE ATTORNEYS, AND EVEN IF WE WERE WE AREN'T YOUR ATTORNEY.
If you want to legally keep the pistol (I'm not even talking about selling/trading it now, merely possessing it), my advice to you is to seek an attorney who deals in such matters Certainly I would NOT advise contacting the BATFE outside an attorney acting as intermediary on this matter. An attorney can do so because your identity would be protected by attorney-client privilege and they would not be able to press charges for possession while you're legitimately attempting to navigate this legal morass.