I was going to post something different but then I came up with a brilliant idea.
Why not make the rewards for adventurers in need "much greater" if they que alone?

For the most part, DPS who que alone for certain things can get really bad que times.
Speaking as a tank though, I would love to help more people get shorter ques even if they are not from my server, but I don't feel the rewards are good enough.

Give adventurers in need that choose to que solo very high rewards based on how desperate the duty finder system is for the role needed. For example, more gold, more soldiery, or even special items that can only be earned by doing this.

If you don't like this idea, maybe take it a step further. Maybe still have the rewards be very high but you can only bring ONE friend to que with you and only also if their role is highly desired. For example.... Two Tanks queing for trials or A tank and healer queing for dungeons.