To my knowledge No. If the firearm(s) already has the required markings such as the caliber, a serial number, where Mfg (Country of origin). The importer must be identified on the firearms as well before it can be transferred to the general public. I have been a firearms importer for over 30...
I appreciate your pics of the fixtures. I find fixturing of gun parts to be as or more challenging than the engraving. Thanks for your generosity of sharing.
I think your best bet for a engraveable o/u is to buy a older Belgium Supposed (B-25) as a starting point. The entry level (Grade I) on these are around the price you are willing to pay. Just a thought.
You might try if the factory is unable or unwilling to tell you what you need to know these folks will know. Tell them what you are wanting to know and for what purpose. I have found them to be better than dealing with the factory.
https://www.colegun.com/