Art Unwin wrote:
"Surely you or some guru can come up with written text that states that
propagation is what determines TOA."

I don`t find TOA in any index. I find "elevation angle", which I suppose
is a synonym, in my 19th edition of The ARRL Antenna Book. On page 2-9
it says:
"The elevation angle is referenced to the horizon at the earth`s surface
, where the elevation angle is 0-degrees."

On page 3-5, the same book says:
"Now look at Fig. 4A, which compares the computed vertical-angle
response for two half-wave dipoles at 14 MHz."

The Antenna Book is not very definitive.

"Transmission Lines, Antennas, and Wave Guides" on page 314 says:
In order to escape from the earth without excessive ground attenuation,
a sky wave must leave the earth at an angle of at least 3-degrees above
the horizon.---At 3-degrees elevation, the distance per hop is about
3,500 km (2,100 miles). Longer distances are automatically broken up
into units not exceeding 3.500 knm."

It`s the medium breaking up the hops, not the antenna.

Best regards, Richard Harrison, KB5WZI