I am not sure about the 3x theory. It would need to be a pretty cheap gun or some very expensive shipping!
Both Diggory Hadoke and I offer a shipping service for pre-1897 (UK antique) guns with our own stock travelling to the US with us. The cost is modest but has to coincide with the shows we attend. No doubt there are others who offer a similar service. You then pay for the US shipping to your chosen delivery address.
Once the gun gets younger than 1896 you will need an export licence and this is when it starts getting expensive.
You will have to pay for UK shipping to the shipping agent, someone to prepare the export licence (you may need an End User Undertaking but this is free, just a pain), international shipping fees (about £170 last time I did one), customs clearance at the US airport (about $390 last time), and shipping to your FFL (or yourself if pre-1899). Finally you will probably have to pay your local FFL for his time and trouble.
The auction houses and better retail operations have this all to hand but most charge on top to cover the inevitable paperwork and subsequent hassles.
John Farrugia certainly offers a comprehensive service and no doubt charges a fair amount for his work and expertise.
