Ok, this is may be a terrible idea, but in my head right now it sounds better than the medal system in the feast. That, and the nature of the random teams, is the main reason I don't like the feast very much.

Sorry in advance; hope this makes sense. I suck at explaining.

The numbers and calculations are suggestions only; can be (should be) adjusted to make it fair, etc.
*Instead of medals, each players are assigned points (or we can call it medals; it really doesn't matter). They have a "worth".
*DPS worth 8 at start; Healer and Tank worth 12 at start.
*Both team starts with 10 points, and gets points only by killing players.
*When a player is killed, the team that killed the player gets all their points/worth automatically. Additionally, the player that is killed loses all their points, and is now worth 0.
*After the killed player points are reduced to 0, a variable is calculated based on the points the player had before they died. The value of the variable is points / 4 (rounded down). For instance, if the player had 8 points, the value would be 2.
*The value calculated is then reduced from the team that got a player killed and added on top of all of the players points of that team as well.
*The player that was killed is now worth 2 points (0 + (8 / 4)), and the other team-members will be worth whatever they were worth before + 2.
*Players can be worth 0 points. For example, from above, if the same player is killed again the new worth would be: [0 + (2 / 4)] = 0. Remember: 2 / 4 gets rounded down. This means the other team-members won't get any additional worth either, as their worth would increase by 0 (duh).
*Players with less than 4 points of worth gets somewhat buffed. If they are worth 0 they get heavily buffed.
*When a team has a lead of 50 points, a total of 70 or most point after 5 mins wins (again, only a suggestion).

Explained plainly: When a player gets killed, their points/worth gets distributed amongst the team-members of that player. The opposing team gets all the points the player is worth added.

Does this make sense at all or is it utter fail at explaining?
There are most likely some cons here, but at least you won't get punished for being skilled. And since players gets buffed at 0 points you won't be killed over and over to avoid that. Tanks and healers should start with a bit more points/worth to make it a bit tactical in the sense of Easy target vs More points.