I think you can do it if cost is not a problem. You could get a lot more magnet into your space. Very small magnets don't use space very effectively. Don't take the magnets too near the centre, use square or slightly rectangular ones , use more of them so the gap is about magnet width at the outside ( they may virtually touch at the center), keep the coils nearer triangular to save space at the centre so that you can get the copper in with the magnets right to the outside of the discs and use thick magnets with good backing iron and make the magnets at least 12mm thick. If you can get to 1000 rpm then it may work.
If you can find details of Hugh Piggott's 2F turbine design, keep similar proportions but stick with neo and scale it down to your size then you should be on the right lines.
For large wind projects you aim for value for money in terms of magnet and copper, in your case you are looking for a working solution and in terms of cost per output it may not be so good but if the final cost is within your means then all will be well.
The Gotwind idea is on the right lines but change the proportions to get squarer magnets, more of them and don't keep the coil holes too large, you won't link all the flux with the inner turns but they will add volts and are short and contribute little resistance,
There certainly are very nice radial design motors about that will do 5 watts at 1000rpm but they will be servomotors or similar and not designed for low cost,
Another factor you may need to experiment with is the winding configuration and the voltage. Single phase is simple but a polyphase winding should do better, my instinct is that perhaps 2 phase may be best but it doesn't lend itself easily to single layer axial windings so perhaps 12 pole 9 coil 3 phase could be a good start if you base it on Hugh's 2F layout.
You will either have to accept a lot of diode loss ( even with schottky) or for rectifying to 12v or greater and using a nice efficient synchronous buck converter for the charger.
Flux