Thanks so much for the info! You mentioned that batteries are not capacitors. That gives me an idea. Would it be a good idea then to put in a large capacitor like a motor starting cap to take the initial inrush of current? If so, would this cap go in series or parallel to the battery? I'm sorry for the somewhat simple question, I have only dealt with small decoupling caps of 10uF or less to filter out noise in the line and maintain voltage. Using a cap to store energy is a bit foreign to me.
In principle you could use a capacitor in parallel with the battery to provide additional short-term current. In practice, the amount of capacitance you would need (several Farads or maybe even a few tens of Farads), coupled with the voltage (too high for supercapacitors, unless you use a lot of them in series), makes it not practical in this case.
I suggest you use a lead-acid battery if weight is not an issue, or a LiPo battery if it is.