I would suggest that u make ctc with a national frt forwarder that have offices all round the country perhaps Burlington air express or danzas aei,
that way you can instruct the company to collect from any uk premises, most big forwarders have their main depot around the LHR area, then the local branch will do the donkey work and then they will truck up to lhr at night, depending on where in the states u want to send the cnmt most forwarders offer a cargo consolidation service which will work out cheaper then going dircet to a major carrier as the forwarder will buy in bulk tonnage which enables the shipper to achive a better rate per kilo, it would normally travel within a 5 day period from door to door depending on the urgent nature of the cnmt, but yes u will have to pay on the volume which is the space it takes up and not the gross weight, most freight fwds will do a charges collect service which wud mean that you could pay for the cnmt on arrvl in the us. if u get stuck pm me x rgds