Featured gamemode punishments?
If you dodge a featured game mode say.... 3 times. You lose the ability to play for 24 hours? OR possibly the rest of the weekend. If you do this for 2 or 3 weekends straight, you may receive a queue ban for the next weekend? Just trying to get creative, because a 3-5 minute lobby time that essentially wastes your time is irritating as hell.
The second suggestion may be a bit out there, but I think the first one is more than reasonable.