The problem: people that selfishly don't try their best once they're in the game
The solution: encouraging those players to try and earnestly do their best without killing too much enthusiasm for the mode (either from lack of extrinsic rewards or creating an uninviting atmosphere)

I think a mixture of the ideas would work best. 1st place SHOULD be significantly more rewarded, maybe even not giving 2nd much or any more than 3rd so that they're clearly hinted to band together.

But, while exp is one thing, the reward should extend to tomes and wolf marks, and wolf marks should have their rewards expanded to include more evergreen exchanges. Obviously they're gonna run out of Orchestrions, Glamours, Minions and Mounts eventually (even if they HAD updated these rewards in the past 4 years) and some players don't even care about those things. There really aught to be more to spend the tokens on beyond that (should I buy my 200th Squadron Meat & Mead thingy or my 20000th Venture?), some of the prices should be rebalanced (15000 marks for ONE piece of materia??), or even just its own version of the GC gacha boxes for each expansion.

Sometimes I vote to dismiss people too, if they're clearly afk chilling at the spawn, but I forget if you can't initiate that when in combat. Also, the matches have been made shorter recently and you need to wait like 5 min or something before you can even dismiss someone (and each player can only initiate like 1 dismissal an hour), so these players hurt more and give less opportunities to replace them before the match stops accepting new players. Maybe some of those aspects could be tweaked as well as the rewards.