I would transfer that to you without concern.
If you can, print out the details page of specs on the barrel and take it to your dealer.
That's what i do if there's any question. As long as i have proof that it's marketed as a "heavy profile" barrel, and it actually is under the handguard, i just keep a copy of the printout with the 4473.
Link if you need one.The issue your dealer is probably having is that the LE6920SOCOM is banned, but the M4A1 SOCOM is not banned. But the real problem is that the M4A1 from colt's current lineup carries the SKU number of... LE6920SOCOM. So the great grey area gets bigger.
And most dealers see the M4 cuts and almost automatically say "nope".
Your other option is to do the 7 day wait for the lower, and just take the upper home... for eh, parts.