The only way it would survive the higher voltage battery is if you put in a voltage regulator to bring down the voltage. Then you could use the extra capacity of the batteries for duration. You would still need to be able to charge the batteries but it sounds like you intend to do that on an individual basis instead of as a pack.

No, I don't know where to get a regulator that would work. It would need to be able to handle to input voltage and the current you will be passing thru it. Powering both the motor and the radio. Then, once the battery gets too weak to run the motor, the radio may also fail to work.