If you are going to buy in the UK and then hand-carry to the US, be sure to ask about the form to get a refund of VAT. I think Moss should handle the form for you, but if not, you will want to do it. They have to charge VAT if they sell in-country, but you can get a refund by filing the form after you export the item.
I've never hand-carried, so can't help there. Having things shipped seems very hit and miss; basically the Customs officer can decide whether to pass it through or put a hold on it. If they put a hold on it, then the shipper will hire a customs agent (broker) to investigate and supply Customs whatever they need to release the shipment. You get to pay the agent's fee, in addition to whatever fee Customs decides is appropriate. Probably 90% of the stuff I've bought from the UK has sailed through without a hitch; but there was a smallish box where I wound up paying $80 on top of the outrageous shipping fee. $20 import duty and $60 broker fee.
FWIW, I have also had them confiscate my luggage when they felt the paperwork was not in order. (It wasn't) But that was electronic equipment, not vintage car parts; and my company had a broker on retainer so it all got sorted out without my being involved further.