Easy solution: Remove the competition element entirely and treat it like the STFs.
Complete the objectives - Get an individual loot bag - leave
If you want to be clever make the rewards based on the entire team's score with an individual loot bag for each member of the team.
Except that STF loot bags are also now DPS based. If you don't believe me, look at your loot when you fly a lower DPS ship. Then switch to a higher DPS ship (I.E. Cruiser to Cannonscort). Watch your loot increase MASSIVELY in value.