Lunar elevation (aka "altitude" in celestial coordinates) is sidereal, so the maximum range is determined by the viewer's latitude. The moon's orbital plane is not perfectly aligned with that of the sun-earth so there's another component there, but this only varies +/- 5 degrees of the sun's declination.

Lunar phase is synodic, so there's no significant variation in the observed illuminated portion with the moon's elevation over one night.

The full moon occurs when the moon is on the opposite side of the earth from the sun, so it rises at sunset, transits the meridian at midnight and sets at sunrise, (+/- a few minutes for seasonal variation).

Here's a nice visualisation of the lunar analemna - the figure described by the apparent position of the moon over a month - from Mt. Laguna at 32.8 degrees north. https://www.hpwren.ucsd.edu/news/20250212/

I also found this page with a decent explanation of the apparent effects of orbital cycles. https://www.cyclecalcs.com/learn/synodic-sidereal.html#faq

even though you are very drunk, you don't assume that spinning around will allow you to se more of the basketball than you currently do. even leaning left and right while looking at the ball doesn't give you much of a different view.

the sun is the door. the moon is the ball. you are a person looking at the ball from earth. leaning shifting left a step might give you a perspective that may correlate roughly with moon-at-dusk. shifting right a step might give you a perspective that is roughly moon-at-dawn.

leaning forward or backward, left or right, drunkenly, and spinning around might give you different angles (relative to the line drawn from your ass to your head) that the shiny-side of the basketball seems to be pointing. but you're just drunk. the shiny part of the basketball always points towards the light above the door. it is just your local perspective that is changing.

Moon follows the sun to the west so to move moon "higher" up in the sky you need to rewind time (15deg/hour). In e.g. 4 hours moon barely moves in it's 28 day cycle so the moon will look exactly the same (you can take a picture and compare). It's the earth rotation that make moon "go down" or up. I've read your article 2 times and I still don't understand what is apparent problem, no wonder AI had trouble. Also it's hard to reason about up and down when moon move along ecliptic which is curve. Down at noon points elsewhere as down at sunset.

As others have noted, there doesn't even seem to be an actual paradox other than a possible confusion about how a half-lit sphere looks from various perspectives.