I will try once more, and then sign off. If a flat-earth theorist wants to accept our invitation, please send me a private message. Transportation costs are out of the question; our Board of Directors won't allow it.
Here's why lunar (or asteroid) occultations are important to the question of the earth's shape.
In the flat earth model, to account for the ~5 degree shift in the positions of the sun, moon, planets, and stars as one moves ~350 miles north or south, you must argue that those celestial objects are no more than about 4000 miles away, from simple trigonometry. Never mind that radar measurements of the moon contradict that argument; let's go with your conspiracy theory for the moment.
The stars must be somewhat farther away than the moon, or else occultations would not occur at all, but can't be much farther because the shifts (as one moves north or south) observed for stars would be much less than for the moon (in the flat earth model), contrary to observations.
Therefore in the flat-earth model, an occultation of Aldebaran either occurs or doesn't occur depending on whether the moon crosses in front of Aldebaran. So any place where both moon and Aldebaran are visible at the right time should observe the occultation, and there would be no difference in the circumstances of the occultation (i.e. where on the face of the moon the star disappears and subsequently reappears) whether you move south or north as long as the event is above the horizon.
What is in fact observed is that some locations on earth see a grazing occultation on the northern limb of the moon, some see a grazing occultation on the southern limb, and locations in between see the star disappear at various points around the moon. This is the effect of the moon's parallax - it is much closer to us than the star is. To demonstrate parallax: close one eye, hold your finger at arm's length so that it occults something you see out the window (a tree, chimney, mountain, whatever). Open that eye, close the other one, and the object is no longer occulted. This is one way we measure distances in astronomy.
The moon's parallax with respect to Aldebaran (or any other star it occults) implies that the star must be very much farther away than the moon. Again trigonometry can give you a (very crude) lower limit to the star's distance based on the precision with which you can measure small angles. But this would further imply that the shift in the positions of those stars as you move ~350 miles north or south on a flat earth would be much less than the ~5 degrees observed - a contradiction that can only be resolved by considering the true figure of the earth.
This coming December 31st offers a nice occultation of Aldebaran by the moon. Try it for yourselves: get an army of flat-earthers to observe the occultation from various (widely-spaced) locations, and bring them together to discuss the results. Sketches or photographs, please. Then let me know by private message whether you wish to engage in a public face-to-face discussion next April Fools' Day.
Farewell, folks, and thanks for the amusing interchange.