This thread could have been answered in one answer, if you provided the much needed current measurements or expected ratings for battery, motor and charger for average and max.
My guess is the charger barely just keeps up to idle motor motor/gear load current with moderate use. I suspect the peak/average load current may be 20x bigger, but then my best guess of duty cycle of a clay pigeon motor is 2% so the overall demand might be 20*0.02 or 40% more .. thus doubling your battery capacity or charger current may be two workable solutions.
The choice is limited by your lack of given constraints for cost or availability of free solutions.
Commercial solutions would consider battery chemistry, electrolytics and pulse current rates for optimal stability and lifetime. The charger ought to be capable of supplying most of the peak current to reduce the aging of battery, while the battery smoothens the voltage. But this is a tradeoff between short term economy and long term reliability.