I did the reverse of this trip, taking about 12 boxes from the UK to US. I used Virgin Atlantic Cargo, and just rented a van at each end. The process was extremely easy and a fraction of the cost of using UPS, etc. I just drove the van to the cargo office at LHR, they unloaded everything and put it onto a pallet, and I picked them up a couple of days later at EWR. The customs process in EWR took a few minutes and they gave me all the forms.

I think BA have a similar service - worth looking into.