Just figured I'd add my 2¢...
I submitted an eForm 1 on 7/01/14 & recently (8/09/14) received my approval for an 8.5" .300 AAC BLK SBR on a Colt LE6921 (yes, it came from the factory as a 14.5" SBR, which I had the dealer de-register & perm. attach a Blackout 51T FH before shipping to my in-state FFL). I too wanted to use LE6921, but this is not engraved on the receiver. Technically, since Federal law requires the firearm to be engraved with the model, unless you ADD "LE6920" somewhere on the firearm, you HAVE to use "M4 Carbine" (in the case of the 6920). People seem to think if ATF approves it, they'll never be charged with a crime. Like how everyone seems to think that if ATF approves their $10, $30, $50 or $100 Trust that it means it's valid (ATF does NOT validate Trusts!!! An approved application is NOT proof of a valid Trust!!). ATF will approve a transfer to an LLC or Corp., but you lapse on the yearly fees & render it invalid, you also render the approvals VOID & subject yourself to unlawful possession.
It's quite simple, manufacturers use internal codes for lots of things. Colt uses the numbering system which honestly has nothing to do with ATF. It is their own internal code. I'm NOT saying that "LE6920" cannot be used as a model number when registering an M4 Carbine, I'm saying that you will unfortunately have to have "LE6920" engraved somewhere on the receiver if that is what you put in box 4d. ATF is approving you to manufacture a firearm. It is irrelevant to them & the examiner if you are building from scrap metal or an existing firearm (save for MGs). What matters is that ALL of the following from your Form 1 matches the firearm:
1) On the Frame or Receiver the Serial number;
2) on the frame, receiver, or barrel the following additional information;
A)The model;
B)The caliber or gauge;
C)Your name or name of the Trust in the case of a Trust (no abbreviations are permitted for the Trust name);
D)The city and state (you can abbreviate the state with the official 2 digit state code)
Think about it like this...
If you ever have to show your Form 1 to an ATF agent & it only says "LE6920" & the receiver ONLY says "M4 Carbine" (on the off chance that the agent doesn't know that LE6920 is the Colt code for an M4 Carbine, what's to stop them from making an arrest? Some may argue that having the original manufacturer's name, city, state, caliber & serial number are sufficient. But if so, then why do we have to specify a model to begin with? Then again, IANAL nor do I work for the Gov. Just taking the law in it's purest most literal form. The law requires a MODEL be specified & the ATF requires that MODEL be engraved on the receiver. Having a DIFFERENT model engraved than what is on your Form 1 may be considered no different than having a different serial number or caliber engraved than what is on your approved app. "I'm sorry, sir. You were approved for an LE6920, not an M4 Carbine.". Perhaps you could just have "LE6920" engraved on the SBR upper. This way you don't have to ship out your SBR lower (a shipping insurance claim won't cover the time you've waited).
Just my 2¢...
PS. I should add that because I submitted an app. for a .300 AAC BLK 8.5" & also selected "M4LE" from the drop down list, my app. required preliminary approval. This was because they had no record of an M4LE in this caliber. I sent an e-mail to Gary Schaible which simply stated that I was swapping the 14.5" 5.56mm upper for a Rainier Arms 8.5" .300 AAC BLK upper. Which was REALLY good since I (some-freaking-how) forgot to fill in the name, city, state, addy info. This was my 5th eForm 1 & didn't miss it the other times. I somehow mistakenly thought I saw everything get filled in automatically as the phone number was auto-filled. Mr. Schaible allowed me to e-mail him this info which he added to the eForm 1 for me & THEN submitted it.