Something like LHR-DUB-PHL /or/ JFK /or/ ORD-MIA-IAH?
Basically picking up another stop in US between the entry point and the final destination.

Ideally adding a transit point near the west coast (eg LHR-DUB-JFK-PHX-IAH) gives the routing +140 TPs instead of +40 for the added transit point, but I don't know if one can backtrack so much since IAH is practically in the middle of the country.