@helvetica that feels hard to do. Brainstorming here a little and came up with multiple scores based on different skills. You could be bad at one type of score but better on others, bonus points to make each score orthogonal to another, like rock paper scissors (i.e. being better at one will affect another).
Grab the best of all teams (or median) and have four leaderboards. One per each skill and one for all best scores combined. Multiple awards ensue plus the combined one. A triathlon of sorts