The US didn't get involved because they knew it would be expensive and economically unsound.
The US spent more on their SST project than we spent on Concorde. We got that fabulous aeroplane for 27 years of luxury Mach 2 transatlantic travel several times a day, they got a wooden mock up.
including the Bell X1 types using our Brit designed super tail system
A myth I'm afraid Peter.
I think not. The Americans were handed all the M52 data, including the unique all-flying tail essential to pitch control at transonic speeds. The only bit they couldn't do was the engine; only Whittle could do that back then, so the Americans used a rocket based on German WW2 design.
Of course if the UK 'establishment' hadn't cancelled the M52 for stated spurious reasons
'Winkle' Brown would have been the first to go Mach 1 some time before the US eventually did.