...if the Earth were a flat surface, everyone in the earth would see the exact same stars and constellations...Sorry, but no.
FET also includes (the incredible) shortening of distances to the stars, etc. Consider that you can't see the same clouds right now that I can, and I think you'll see how they manage to make a bit a sense.
I hope that helps.
Sorry, but yes.
If the earth is a plane, I would be able to see polaris with a telescope from anywhere in the surface, the same as I would be able to see the clouds in New York from Berlin with a telescope, excluding the obstruction of buildings and mountains, as well as the atmospheric distortion.
But from South Africa, I can't see polaris or any othe star in the northern hemisphere, according to my observations or anyone else's observations.
If the flat earth model proposed is a semi-spheroid over a flat ocean, then you are not talking about a flat earth, but rather a semi-round earth. In this case, all your model from its foundations loses its validity since you are applying plane theories and maths to a curved surface.
Also, given your argument that the distance to the stars noticeabely change, I must ask what method is used in the flat earth model to measure the distance to each star.