Question about Voltage in my home-made speakers.?

The 10.7 VAC is what is coming out of the secondary windings of the transformer. As it is AC, there is a rectifier inside the speaker that is converting this current to DC. You will have to bypass that and determine what the final voltage (and current requirement - Amps) are being supplied to the amplifier circuits in the speakers. Then, and only then, will you be able to be able to add the appropriate resistors to supply the amplifier with the correct voltage from the 12 Volt battery. A volt or so in either direction is usually of little consequence. This is more complicated than you thought it would be, isn't it?