I'll just post a quick reply on my initial thoughts - I'll be back in about half an hour or so.
First off, it's been a while since we spoke. I trust you are well.
On reading your explanation, my initial impression is that we are at least on the same page in terms of the way we are looking at the problem. I think that's a hopeful sign that we can have a fruitful discussion.
In the period since we last spoke, I also prepared my own explanation, and it takes a very similar form to yours. It struck me at the time we last discussed this (and I guess you too) that this would be so much easier with some pictures to illustrate. Mine are up on my website, with my own explanation, here:
http://www.boredhugekrill.com/moon
although we're looking at the problem in the same way, there is one significant difference I can see: your explanation has the Earth orbiting the Sun clockwise (assuming celestial North to be "up" in the picture), not counterclockwise. I believe that is incorrect and why you arrive at the conclusion that the Moon should have been at its highest point in the sky, not its lowest, at the first quarter around the time of the autumnal equinox.
Your diagram is this:
my equivalent is this (sorry about the background being unsuitable - I'll try to fix that and edit later) (edit - now fixed):
Regards
Krill
(edited to fix background on my diagram)