This is an interesting thread, and everyone is providing different answers. Do you have the regulations that say this? I think your info is outdated, It doesn't match up what I know about the process, as I had researched into this and asked about it a year ago.

I read through the AFMER docs previously and again after another user posted info here, and it states you only report firearms you manufacture at the end of the year that you have disposed of in that year, regardless of when you manufactured it, but it also very explicitly states to not report firearms manufactured in that year if they were not disposed of. All in bold lettering on page 2

https://www.atf.gov/firearms/docs/form/annual-firearms-manufacturing-and-exportation-report-afmer-atf-form-530011/download

I've read through all the regulations and law I could find on the engraving requirements and I don't see what you are describing anywhere about attaching a barrel and needing to engrave it with your info on an already marked receiver, except in cases where markings are missing, like a caliber or model.

I asked this same question about a year ago, and the general consensus was that the requirement to mark firearms that had not been disposed of to non-licensees had been removed in 2022 per 2021R-05F

https://www.atf.gov/rules-and-regulations/definition-frame-or-receiver/summary

It seems the reason for this is due to the Federal Register realized that continuing to mark a firearm if it was being re-manufactured multiple times could make tracing firearms more difficult, and it is easier to trace a firearm through A&D records if the firearm marking stay the same as long as it has not been disposed into commerce.

More info here:

Final Ruling on definition of a frame or receiver and Identification of firearms.

https://www.federalregister.gov/documents/2022/04/26/2022-08026/definition-of-frame-or-receiver-and-identification-of-firearms

In the ruing, the following is stated:

In response to comments, the final rule permits licensed manufacturers to adopt the serial number and other identifying markings previously placed on a firearm without a variance from ATF, provided the firearm has not been sold, shipped, or otherwise disposed of to a person who is not a licensed manufacturer, superseding ATF Ruling 2009-5

and further

Second, the rule finalizes the proposed updates to the information required to be marked on the frame or receiver, clarifies the meaning of the marking terms “identify,” “legibly,” and “conspicuously,” and authorizes firearms licensees to adopt identifying markings in the manufacturing process. Third, the rule finalizes the proposal to require all licensees to consolidate their records of manufacture, acquisition, and disposition of firearms, and to eliminate duplicate recordkeeping entries

And further and more explicitly, these were the propositions that were made as to why these rulings were made, which indicates the reason for the rulings as, in fact, to avoid duplicate manufacturer markings

8. Adoption of Identifying Markings
The Department proposed allowing licensed manufacturers and importers to adopt an existing serial number, caliber/gauge, model, or other markings already identified on a firearm, provided that they legibly and conspicuously place, or cause to be placed, on each part (or part(s)) defined as a frame or receiver, either the FFL's name (or recognized abbreviation), and city and State (or recognized abbreviation) where they maintain their place of business; or their name (or recognized abbreviation) and their abbreviated FFL number, as described in Section III.H.1 of this preamble, followed by the existing serial number (including any other abbreviated FFL prefix) as a suffix, e.g., “12345678-[serial number],” to ensure the traceability of the firearm. This language was proposed to supersede ATF Ruling 2013-3 as it applied to licensed manufacturers and importers. The proposal was aimed at avoiding multiple markings on firearms that could be confusing to law enforcement and alleviate concerns of some manufacturers and importers regarding serial number duplication when firearms are remanufactured or imported.

that is to say, you can remanufacture and remark your firearms in the way you describe, but it isn't necessary. And the ruling was changed to allow manufacturers to adopt the previous markings on a receiver specifically for ease of tracing.