[Is] there possibly a way to generate enough power? An alternator/magneto combination, perhaps?
Not according to the law of conservation of energy.
Magnetos are for spark plugs in piston engines. If the airplane is fully electric, then you don't need magnetos.
As for the alternator, if the battery has 100 pirate-ninjas, and it spends 1 pirate-ninja to turn the propeller and turn the alternator every minute, the output of the alternator will be a tiny fraction of that pirate-ninja.
For electric propulsion topics here on SE, click here.
For the first question, click here.
For a list of modern light electric planes, click here.