M58, et al,
Cross docking adds significant costs to transportation but is certainly one solution. Another is 'trailer swap'. Have companies enter agreements to haul the trailers in their own country. Example : USA company X take a load to Brownsville and drops the trailer, then Mex company Z hooks up and takes it the rest of the way into Mex. Meantime USA company X picks up a trailer from Mex company Z and brings it into the US.
I understand the cost issue, but my trailer drop morphed to cross docking as I added the idea of trailer quality issues and the opportunity to inspect or oversee loads. However, the trailer swap is a good idea on its own.