Given the nature of the capture fight, and the fact that are 4 attempt per person limit, I take it the proper way to maximize reward is for everyone to only fight it once, wait until the last 10 minute, then go free for all?
And if the group is strong enough such as a single hit from each person is more than enough to kill it (so not everyone have a chance to tap), then the tap must all be made with a week team and real damage only done in the last 10 minute free for all (which is 3 per playre, if 1 per player is "too much", 3 per player will kill it easily)

10 minutes should be sufficient for 3 fights, even if it lasts 10 rounds. If there are issues that c*ways be expanded to 15 minutes.
Frankly, the difference between 1st rank and last place is negligible, only 80k coins and 15 coupons. So hopefully getting everyone to work together won't be too hard.