Well no infinite cylinder Earth is still flat earth because remember I said that the cylinder is just a projection of 4D loop. If we were too fly high above such earth we are not going to see an actual cylinder we would still be flying over flat plane. The cylinder is simply a mechanism not a physical object in space.
So now you switch back to a cylinder and ignore the globe.
Then you switch back to all the problems with it.
Again, with such a setup there is no need to appeal to 4D, it works perfectly fine in 3D, it just can't be embedded in 3D Euclidean space.
But again, that would mean not only does Earth repeat, but so does the sky. That means you would be able to see multiple copies of every object in the sky, including the sun.
But you can't see multiple copies, and thus this model is wrong.