I believe the description of US BATF and customs is correct, but believe yo maybe missing the rules and permitting from the UK which I believe now includes Individual export licensing.
As much as I believe do it yourself seems a more comfortable way, but do not think it likely a good way to go.
I think cost wise it is best to employ an experienced importer and have the patience to allow the export licensing from the UK and US customs and BATF paperwork to be done by them.
As for cost on top of your purchase I believe you are looking at $2k or so over the purchase price (depending on the value of the gun, more if you have to pay customs on a $10k plus gun)
The most cost effective way is to allow an importer include your gun in a bundled shipment, which while slowing the process, keeps costs down. Speed costs money.
