Join In Progress Idea.

[Curagaja]

No one would join except for the final boss for the best stone drops.

This might be true for the tomestone dungeons, but not necessarily for the others.
A (potentially rare) case that might come up due to this would be the Join box showing Time remaining: [75:24] (or something high like that) with Progress [2/4] and realize that those remaining in the dungeon were doing a great job of clearing it, but some important role had to leave which put them at a stand-still. The player searching would decide immediately to join and keep the party going knowing that he got into a good group before he even clicked join.
The counter-argument to this would be Time remaining: [30:10] (or some reasonably low amount of time) Progress: [2/4]. The player searching would immediately notice that this party is incompetent when it comes to the dungeon and would cancel their application immediately. But I don't see this affecting anything. If the player was unable to see this until after they joined, then they would join and leave as soon as they notice time remaining and progress complete. Those would be almost the exact same situation.

Edit: Typo 1/?