This looks like it could be a fascinating idea. I'm a fairly visual person though and it's kinda hard to picture. How are you at drawing diagrams?
If the cylinder is standing up with one of the flat ends resting on Earth, does that mean the celestial bodies occupy the other flat end? Or are they wrapped around the sides too?
I'm basically imagining it as that the celestial bodies are on the top end of the cylinder, and that it is the curvature of space that makes it appear as a dome in the sky. Can this explain why we observe the stars rotating about two celestial poles? And if so, (and maybe this is the exact point you're trying to make) how is this any different from just saying "the Earth is round"? Would space travel work as we normally think of it in this model?
To be honest I'm not enough of a physicist to answer all the questions specifically, but I can provide a sort of diagram.
I'm also leaving this a little bit open. It can be interpreted that celestial bodies are on the other side of the cylinder, or that they are suspended in the middle. Another interpretation is there is only one end of the cylinder, and it extends infinitely upwards, and all Celestial bodies reside inside of it.
As far as space travel goes, there are two possible outcomes I can see based on how you navigate. Basically, one is that if you attempt to straight in one direction on the x or y plane you will simply circle around, as the celestial bodies do, and the other is that you might hit a wall or leave space, the same consequence as attempting to cross the south pole in the FE model.
A possible model of FE space:
Another possible model of FE space:
Yes, if you want to get pedantic to the point of inhibiting discussion, you are correct. However, the terminology that we use is an easy way to get across a point that is almost universally understood. Flat and round.
That's not quite my point, though. The definition of flat doesn't matter; that was just a sample to explain my thought. Say Planar and Spherical Earth to avoid it, if you'd like. My point is if they both equally provide a understandable definition of 3 dimensional space with a model of physics that describes interactions between objects in the same way, then there is no real difference between the two models other than basal frame of reference.