It should be fun to watch what develops, here and elsewhere.
You may be in the wrong community then. It is a different Flat Earth community which says the Midnight Sun is impossible. This community has always accepted the Midnight Sun in its models and portrays several mechanisms in its materials, which relay that the Antarctic midnight sun has been in Flat Earth models since at least the 1920's. Even in the classic Monopole model, the magnifying dome demonstration for the seasons
appears to make a midnight sun.
It's also plausible that our official celestial model for Flat Earth, the
EA Model, could be extended predict a midnight sun. If the light of the sun actually takes the shape of something similar to the closed loops of magnetic field flux lines, it could be that the earth is interrupting the natural path of the Sun's light and that the rays on a larger scale could loop around and appear to be coming from the opposite direction to a distant observer.
If we take one of the upwardly bending light diagrams in the link above and simply extend the loop of one of the rays which intersect with the earth, it loops around and appears to be coming from an opposite direction.
This isn't new, and I have my own questions about the particulars of how this dipole shape would appear, but the above appears to demonstrate that a midnight Sun is not an impossibility in current constructs.