[Christ]

The design I have in my head is basically a stack of magnets oriented north facing south, passing through several stacked coils. The variable and unpredictable stroke is really at issue here, so it may be best to make each coil capable of providing the necessary voltage by itself, so that shorter strokes don't 'miss' producing the correct voltage to drive the circuit.

In other words, each stacked coil provides, say, 14.5 vdc @ 500ma, so a longer stroke just boosts the amperage in the circuit by passing more coils through more flux lines, but a shorter stroke will still produce the correct voltage to power the circuit, despite being less 'driven' in terms of charging ability.