Try your existing Amtek with a 6v battery and see if you get acceptable output. You have reduced your chances now by reducing the blade length. ( power goes up with square of rotor diameter)

If it works well enough at 6v then you have found your problem and have lots of choices ( probably none of which you will like).

As Tom said it is virtually impossible to charge at 6v and take load at 12v at the same time. You can use a boost converter to raise the voltage from a 6 v battery or you can boost the generator output to charge a 12v battery. ( loss incurred in either case).

You can rewind the motor to cut in at lower speed but it is not a simple undertaking and may in fact be difficult depending on the commutator connections ( probably staked or crimped).

You can build a low speed alternator to suit the miserable blades or you can build a decent set of blades from wood that will work directly with the Amtek as it is.

I think you need to keep prop diameter up in a poor wind area rather than trying to raise speed with a small diameter, which makes your wind problem worse.