Honestly, the solution is fairly simple.

Just make a queue that is for people waiting for an in-progress run. The wait times will be longer but at least people wanting to do full runs can go on their business and people who want to do partial runs can go on their merry way. The waiting for in progress queue would probably be a much longer wait (since they are waiting for full parties to lose someone either by kick/dc/or other means). So, after about 15 min, a pop-up window should appear and ask the player if they'd like to form a new party or continue waiting for an opening.

Now, a few changes. Don't show the progress in a dungeon. Why? Well, if you do, you'll still get the issue of people withdrawing. Just pull the player in. Once they are in they have a choice to withdraw...with the normal 30min duty finder penalty for being the first to withdraw.

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Also random side note, holy crap to the people asking for bans. Prime example on why your community should never be listened to for any sort of development suggestions. Banning, seriously? What a horrible, horrible solution.