This is just a thought, have you considered using a smaller wire with more turns, making the coils much narrower and increasing the coil count? Treat EACH COIL as it's own "phase"? Yes, I know it would take a fair number of discrete diodes (Two per coil), but diodes are cheap. I am thinking of maybe 18 to 24 coils with 200+ turns each of #22 to #30 wire. All coils would be in parallel, so simply increase turns & decrease wire size until you get to the voltage you want, then increase coil count until you get to the amperage you want. You could test this with a single coil. 24 coils @ 0.7 Amp each @ 12V = 200W. Using this approach, you could also increase magnet count (in pairs) w/o regard to coil to magnet ratio.
My thinking is that in your very small form factor with your small magnets, you might improve efficiency even though it appears you are increasing your IR losses per coil. I am picturing "non-tapered" (straight) coils wound around 1/8in round stock at either end with an inside length of 2in and a total width of less than 1/2in.
I HAVE NOT done any calculations on this for physical feasibility, and obviously I have not tested the theory, it is just a thought....but I am curious :-) Maybe I will get a-round-to-it and give it a try :roll: Sigh, sadly,though, now I have to go to work :cry: