Just give a bonus reward proportionnal to the lack there is. Here, problem solved.

If there is such a throttle in tanks that dps and healer need to wait 30 min to get a queue, give 10k bonus to tanks. Tanks get in, queue get reduced to 5 min for healer/dps ? 500 gils bonus to tanks. So many tanks got in that now healer is the throttle and tank have to wait 10 min ? Give 2k to healers. So many tanks and healers than now dps have an instant queue ? Not going to happen no matter what.