for a similar thrash across the pond with a full load (35t) the 340-300 will go straight to 370 ex JFK, (and 360 ex LHR. ISA conditions). Slowly though, about 34mins for a C2 powered a/c and 29mins C4.
An ATC buddy of mine has figured out how the A340 manages to climb. It is because of the curivture of the earth.