ermm I would look at 2700mah + battery what voltage is up to you. I fully drained a 2200mah battery using 550 motors x2 for drive and a MY1016 for an axe (so not contain draw) in 4 mins ish. Michael did you take part in the Featherweight play time at Manchester, if so do you remember how long that match was ?
I didn't have a active weapon (much to my annoyance) but I ran separate batteries in The Honey Badger 2 for the drive and weapon for this reason. My 775 motors will go the distance on 2100maH batteries (2x 2S1P LiFePo4 batteries in series) which worked perfectly well... ish.

I did take part but I wasn't in there for the full amount of time, my batteries packed up about halfway though (wheel was binding on the bodywork causing a major drawdown on the batteries). I think the whole thing was at least 6 minutes from what I recall.