Ok, heres something I just thought of, however couldnt work out how to narrow it down to be searchable...
Your flat earth, you all believe to be some sort of conspiracy. Its a disk that shoots upwards at a uniform accelleration, as does everything else around it, and theres no other possible explanation for it.
really its a stupid concept IMHO
However, with all this conspiracy talk etc, and so many unaccountable explanations for so many different things, you're more likely to have this as a model:
The whole flat earth is a cordoned off section of a much larger planet. It has a large wall as a boundry, possibly some sort of dome over the top. This would explain all the inconsistencies with your physics problems, because gravity and everything else would be a result of the overall planet, as would volcanics and tectonics. Also, the natural curviture of the earth could be explained easily as its a portion of this other planet.
Still, however, if you where to turn around and believe that, I would be very very worried about your mental state. Seriously, to believe that you're contained within some huge wall with no means of escape and everythings a conspiracy, you'd have to have had some deep, deep psychological traumas as a child that lead to some crazy arse insecurity problems.