And the Q of a hamstick is probably a lot closer to 50
than to 500. Someone else reported the hamstick as -20 dBd.

I would think it would be hard to design a coil with a Q of 50.
I tried to find a picture of a Hamstick to estimate the Q,
but no luck. Anyway, assuming the Q is 50, NEC returns
the following results:

Structure efficiency - 5%
Total radiated sky wave (with 100 W in) = 180 mW.
Input impedance - 112 ohms.

73,

Frank