The modern day flattists went the way of preserving timezones, and sacrificing sunrises/sunsets and some stars being visible only on one hemisphere.
Of course, they aren’t admitting to the second part. Usually they just scream “PERSPECTIVE!” at the sunrise/sunset, and I don’t know what they even do for the stars. Probably just declare them fake news.
IMO they should just have gone with the classic “plate with sun going around it”, and then say that the firmament has a refractory index gradient in just the correct way, that it takes longer and longer for sunlight to reach you, the farther west you go. At the westmost edge, you are just seeing yesterday’s sunrise as the actual sun is setting next to you!
Of course I’m bullshitting, but that still makes more sense than their hovering spotlight sun looking like it’s setting, because perspective is magic.
Edit: and, of course, the most important super-logical megaproof:
If Earth was flat, the cats would have pushed everything off it by now!