Might be a silly question - but do US border staff have to be US citizens? So would have to be flown out and work as an ex-pat and not recruited locally?
Immigration seems not a particularly skilled job, pretty much computer says either "yes" or "no" and the demand to "put your index finger here". For the US ones, the main skill seems to be an excellence in extreme arrogance and ability to talk down to every pax as if they are a criminal.
Why can't the US recruit local Brits to do this and train them in these "skills"?
I'm not sure you could find a menacing enough British immigration officer.