I don't know where to start.
"Can you elaborate on that point? If I have an oval coil of wire 1" x 2" in shape, how is the voltage/current different if I have 1" neo disc cutting through compared with a 1" x 2" rectangular block cutting through the coils. I know that only the magnetic lines cutting perpendicular induce a voltage, so is it fair to say that the rectangular block (same thickness, and grade) would have more flux and induce a higher voltage?"
If you start going down this cutting lines perpendicular route you will get completely bogged down. Just think of flux linkage and life is easier. If you link all the flux then area is the thing that matters.
Assuming that the 2" diameter magnets are 1/2" thick same as the rectangular ones then the 2 " dia have an area of 3.14 sq inch. The rectangular have an area of 2 sq inch. that is why the round ones do better. I don't particularly like round ones and they are significantly more costly than the rectangular ones. I personally would use more of the rectangular ones but as you are intending to use an existing design then the round ones are a better option.
For round magnets I cant help suspecting that the best shape for the coils is round but when you just replace the rectangular magnets with round ones on the same disc size the magnets are too close together to use round coils. Squeezing the things oval gets you more copper in and the loss of flux is tiny, the bits where the magnets nearly touch have little area and there is a lot of leakage flux so not linking that bit effectively makes little difference. The magnets are not used to best advantage but Dan has found that the round magnet version is significantly more powerful than the rectangular one so the use can't be that bad.
For the same thickness the shape matters little, to get more out you need larger area magnets or more of them, either way more magnet area means bigger discs if you want the full advantage.
The stator burning out is an issue of man, not the type of alternator. Your conditions are different as you will have some form of mppt but just for the record with the normal directly connected battery scheme if you go for a very low cut in and make the alternator efficient it will stall in high winds. The only way to keep the low cut in and get away from the worst of the stall is to make the overall efficiency less than 50%. This way the power you gain from matching the prop curve far outweighs the loss from low electrical efficiency.
If you choose to cause this loss within the stator it will get hot and how hot will ultimately depend on how well you get the heat out. You can play tricks with not potting things, play with air flow, fans, holes in coils or whatever you want but the thing inherently is not going to cool as effectively as a machine with coils wound on iron poles where you have thermal conductivity from copper to iron to an exposed surface. That may mean that you can push an iron cored machine harder for less risk of burn out but the system efficiency is usually lower for the iron cored machines.
The axials don't burn out if you keep within sensible ratings, most don't furl safely. If you want more output then just make the alternator more powerful and add the electrical losses outside, not in the stator.
In your case the heating will not be such a problem as your voltage will rise with load. What you are hoping to do is exactly the same as Halfcrazy is doing with the mppt classic controller. The standard 10ft machine is doing near 3kW when its realistic rating for direct battery charging is about 600W ( 700 -800 pushing it)
Winding for the higher voltage is just a case of using more turns of thinner wire. If you want to stick with the standard tried and tested design use the round magnet version in preference to the rectangular unless you want to go to N50/52 at far greater cost and reduce the turns and use thicker wire relative to the N35 design.
For a given gap length the flux depends on area and magnet grade. The other option is use thicker magnets a wider air gap and then you have more winding space for the same number of turns. There are so many choices but it is wiser in the end to stick to something tried and tested unless you really understand the whole concept, so many things interact and just changing one thing usually messes up several others.
Flux