I've dealt with some auction houses that require the gun to go through a FFL because they can not definitively prove that the gun was made prior to 1898 due an absence of records that have disappeared as has happened to many English makers.
Unfortunately that happens and as you say they can't be blamed. Not much to be done in that case other than proceed through the full FFL process. With regards to records there are occassional guns I don't pursue because I can't find records that would "prove" to the ATF or other parties the age of the gun. Generally I find that if the maker is listed in Brown's Vol. 1 - 3 , then I've been able to get either an ATF sign off or import as an antique. I've found ATF also accepts published articles on gunmakers covering model ages. Not much help if a third party is insistent but it might be helfpful for those that can be persuaded.
As an aside, permitting and antique/curio&relics designation and permits are is something the exporters I use in the UK generally check as they seem to require it be confirmed as part of their export permitting regardless of the designation in the UK. A decade ago some would just ship an antique direct but no longer. Paperwork is now required but in the long term is just a hassle not a problem. Funny to sign off on official declarations that I will not use the guns in the assembly of nuclear weapons, as if anyone smuggling such material would be honest, but that's the way it is. Oddities occur for instance with the purchase of damascus barrels which are still handled as "firearms" in the UK with the requisite RFD transfers required.
Jeremy