"The whole thing is made of wood. "
That is your problem. I assumed that the magnets were at least on a steel disc even if it was a single rotor.
With coils 1/4" thick and 1/2" thick magnets you would see a big improvement with the magnets on a steel disc.
Even more is to be gained from using a second spinning disc to complete the flux path.
Before the days of neo you would never be able to make any sort of alternator at all without working the magnets in a closed magnetic circuit. It becomes possible with neo but you are degrading a high grade magnet material to something little better than the old carbon steel, it just doesn't make sense.
Yes I did roughly calculate your useful flux at something like 80mT whereas most of these machines are working somewhere just over 600mT.
You gave me number of poles, speed, number of turns and volts so I just worked the emf equation backwards to get flux density.
Flux