Walter,
You said:
"When power P is delivered to the
antenna and all of the power radiated is then integrated over the entire
hemisphere, the integrated power will equal power P exactly. Now, because
all of
the power delivered to the antenna is radiated, any increase in radiated
power
due to some change in the configuration of the antenna is impossible.
Therefore,
this constitutes proof that your claim of gain with the EH configuration is
invalid."

I disagree. I think all you've asserted is conservation of energy, not
whether or not the antenna has gain.

Joe
W3JDR