I'm not familiar at all about that particular type of motor, but a lower gear will make your climb up the hill work better, but slower. Slower all the time, not just on the hills.
More voltage, if the controller can stand it, will make the motor spin faster. So combining more volts with the lower gearing could work well. If your controller cannot tolerate 36v, maybe it can still take 6v more.
Too bad it's not easier to peek inside that controller, if you see capacitors inside labeled 50v, I wouldn't hesitate to run 36v. 36v, fresh from the charger is actually about 42-44v. The caps look like little soup cans.
Climbing really steep hills with an ebike is not what most are designed for, so you are far from alone in being dissapointed with the performance of 600w. Most of us that tackle steep hills with ebikes use 1500 watts or even more.
Amp hours is the capacity of the battery, like the size of the gas tank. The controller regulates how many amps flow from it, like the size of a carburator. Watts is amps x volts. So if you can increase volts by 25%, you'd have 25% more watts.
THE LIPO RULES. NEVER ABOVE 4.3V NEVER BELOW 2.7V DON'T PUNCTURE
Ideal charging /discharging range for Lipo, 3.65v minimum 4.1v maximum
See battery technology section, FAQ thread at the top of the page for lipo noob info.