So this disc thought experiment... I'm visualising a massive disc, basically the size of the observable universe. It's rotating very slowly, however it is so big that the velocity at the edge is massive, relativistic even. Assuming the disc is strong enough (lol), and assuming constant rotational velocity, oh and also assuming the observer is fixed into position and is an infinitesimal point (fuck you tidal forces), the observer wouldn't notice how fast he was going. In fact from his pov, he is stationary and the centre is rotating around him at relativistic velocity. From his pov, time is normal, while the centre is dilated and in a slower time reference frame.

One of two things is going to happen... either the disc appears to be stationary, or an observe at both the edge and the centre would observe extreme spacetime warping, resulting in an ever-tightening spiral. I'd guess the latter.

Definitely headbending.