Hmm, you have a motor that's designed for 220V, and you don't want to stack up the batteries to match that. I suppose you could take all the wire out of the motor and rewind it, but by the time you finish that, you could have bought one to match your battery.
Assuming, contrary to your statement, that you're okay with stacking batteries, cheap AC tools and appliances might actually work pretty well. The key here is the "universal motor". Basically, it's a DC motor just like you'd expect, with coils that rotate and take power via brushes and a commutator, except that the permanent magnets in the stator are replaced with more coils. This makes it run the same direction regardless of electrical polarity, which means that they can also work on AC. And they can still change direction by flipping either the stator's polarity or the rotor's, but not both. Thus, a reversing AC drill might be a good donor for an easily reversing, high-voltage DC motor.
Make it lighter. Attack it with a drill, sawzall, or whatever. Just get rid of as much material as you can without compromising the structural integrity where it's needed. It'll be more agile that way, in addition to using less power and extending battery life. (or you could use a smaller battery, which would make it lighter still)