Would the best ever circus tumbler jumping off both feet always beat
the best high jumper jumping according to IAAF rules off one foot. 
This was proved on BBC TV Record Breakers in the 1980s but I can find
no proof

Good question.  I have wondered about this in regard to gymnasts' mat routines.
It seems like after a couple of flip-flops that the extended double
flip might allow them to clear a bar higher than the best high jumper
can.  In theory, I admit, they could probably never coordinate the
run-up so that they didn't hit the bar, and maybe when they rotate
there is no way for them to leave space so that they rotate around the
bar.  A slo-mo video should should be able to reveal  which height
they "clear."