A while back I had a bit of a look at the logistics of Polaris, and was disappointed to find that, provided there is some force pulling light away from Earth, a Flat Earth can provide an explanation for Polaris.
I disagree. EA is an attempt to explain what we observe with Polaris, but it doesn't work. The problem is that, barring tiny parallax movements, all of the stars retain their angular separations as they move around the pole stars - measure Orion, for example, and then measure it again a few hours later, and although it will have moved, the distance between the stars won't have (it's a roughly 10x20 degree box, if I recall correctly).
Then take the problem that, if we assume a flat earth and triangulate polaris in an attempt to find its range, we will get a different answer depending on which latitudes we choose for our two observation locations. So FET wheels out EA in an attempt to explain this, but the problem with that is there is no way for EA to operate that would simultaneously explain the apparent triangulation problem whilst also retaining the constant angular separation of the rotating constellations. If EA was bending the light, then our rotating constellations would change shape as they moved around the sky. But they don't.
The south doesn't have a star over the south pole
Yes, it does. It's called Sigma Octantis. It's not easily visible without a dark sky and/or some kind of magnification, but it's there, and it behaves the same as Polaris - your latitude = its elevation angle. The Southern Cross is actually quite a long way north, at a declination of around -60.
Your point is entirely valid though, and there are several threads running elsewhere to this effect. I showed on one of the recent ones that its actually possible for Sigma Octantis to be visible after dark in Africa, South America and Australia at the same time, albeit for a very brief window. I'm still awaiting a reply from Tom on that.