The coil is the main killer.
Air core has the least concentrated flux... You could stack those magnets until you're blue in the face, it's gonna be a diminishing ROI if the magnetic circuit isn't tight enough.
Achieving that isn't quite what it appears by simply "flipping an axial PMA inside out" with 1 magnet and 1 air coil (or even one on each side).
In an axial PMA, the flux is tightly controlled by the discs and magnets themselves, causing it to "beam across" the gap, which significantly offsets the inefficiency of the air core. In a situation like the bike, the flux is dilute and "flairs" out as it leaves the poles... maybe "aimlessly" is a decent word. Closing it up (look at the brakes for an immediate visual on my kneejerk thoughts) will help tremendously.
That's also an awful physically small coil. You're cutting the turns with a much larger diameter "slice of flux" than the coil, which just further dilutes it's potency and with that kind of difference in diameter, probably is even causing self-canceling effects. An air core coil doesn't have any means of directing the flux thru the center so it cuts more efficiently, so this won't work.
One more thought comes to mind for when it's on the bike... the rim, being steel, is going to also steal some of the flux and short it out... difficult to work around since you can't put a pair on either side even to gain a useful pole out of them, because of the brakes.
This is one of those "what works in the classroom needs performance tweaks before it's useful in the real world" deals. If you were looking to read RPM, I'd say you're on a reasonable path, sorta... Any kind of real power, no.
Steve