A couple of issues that I don't think have been covered (please forgive me if they have):
The definition of antique in the UK is 2 years different from the USA. Any gun made AFTER 31st December 1896 is deemed a NON-ANTIQUE and is subject to an export licence. The application for this must be supported by an End User Undertaking and although the licence is issued for free by the UK government department, only someone registered on the government system can apply.
One way round this is to use someone with an 'Open Export Licence'. They will by necessity have a regular number of firearms being exported to the country in question and they must all travel through the same US entry port and FFL. They are by definition experienced in these matters, Harry Gordon is a good case in point. You will still need an End User Undertaking.
The licencing authorities are aware of the difference between the UK and US dates and will issue an export licence without a Form 6 if one explains the situation. Otherwise a 'Permission to Import' is required, ie an FFL Form 6.
Secondly, the cost of air freight from the UK has increased hugely recently as all the airlines are charging a 'lock up' fee of at least 100 ($160) plus increases of fuel surcharge etc.
I had a nice 1910 28g Westley Richards planned for export recently but because it missed the economies of scale by travelling with my antique guns, the export had to be shelved for the time being. Export costs were heading to $1000 or more including all the US end. And I have all the contacts but needed it there quickly.
Lastly, VAT is NOT recoverable on the buyers premium. Only VAT on the hammer price as specified in the catalogue is recoverable and that is subject to a time limit. So unless the catalogue says the 'VAT is chargeable on this lot at 5% (or 20%)' you can not reclaim the VAT on your invoice.