It took it's time, to follow these argument, but in the end - for me - it appears quite simple.
You know this diagram from
http://www.sacred-texts.com/earth/za/za32.htm ?
The distance of the vanishing point - aka the horizon - is defined by the limited resolution of the naked eye, where lines from the observers eye E to the vanishing point H and the surface C to H build an angle less than 1 minute of degree.
Rising observers position will broaden this angle and move point H (horizon) farther away, until the 1 minute criteria is met again.
But what, if observer has "hypervision" and could resolve angles less than 1 minute. Is then the point H also moved farther away?
Anyone can get "hypervision": use a binocular or a telescope.
If e.g. the binocular has a magnification of 7x (standard marine binocular) according to this the horizon should be 7 times farther away.
I frequently use such a binocular at sea, but the horizon always appears to be at the same distance, no significant difference when looking with naked eye or with the binocular - unless details get clearer.