Yes there is indeed a problem with space at the centre if you try to use a standard hub.
Increasing disc diameter is a way round it. Few people look at the waveform on a scope and would never worry about what you see. I think your waveform is rather worse than usual because of the large magnet spacing and small coils. Things will be better if you wind bigger coils so that they touch as in Hugh's version. In reality it gives you more winding space. I suspect the waveform is likely to be worse with single magnet rotor especially if the coils are thick.
There is normally a lot of third harmonic in a single coil waveform ( and of course in the phase voltage). It is uncommon for the harmonic to exceed the fundamental, but it doesn't matter that much. The line voltage of a star connection will be much nearer a sine wave as in theory the 3rd harmonic cancels.
Try making your coils bigger by winding on more turns until they touch and then just live with the waveform. Such a bad waveform makes it a bit difficult for you to decide on what to take for your cut in speed. Some strongly advise the use of a scope but I find it adds confusion. I use a mean reading multimeter scaled rms ( the normal cheapo type multimeter) and just take its reading as though it was rms ( not accurate but works near enough). When you rectify that lot the waveforms you see will be pushed into insignificance.
There are a few combinations of coil size and magnet spacing that get reasonably sinusoidal, but usually there is a large 3rd harmonic component, either in phase or out of phase depending on the spacings. I really don't think it is important.
You probably need to keep near Hugh's number of turns but use thicker wire to make bigger coils or you may do better to use a similar size wire and make the stator thinner to get fat coils. Thick stators are not effective with this single rotor type magnet.
The hole in the magnet will have no effect that you will ever see.
Flux