I like the idea as is. But I would add some things:

The Safe Point actually stops the duty clock if everyone is standing in the area, but only when it is active (meets OP's requirements of less than full party). This can have its own limit. But I don't see any way to exploit the duty clock, I've never seen a group be hardpressed to meet it unless it has frequent disconnects or other issues.

As well as an option to receive exp on the class you queued up for. If I'm a Ninja and queue as a DPS. But have to switch to Paladin to finish a dungeon. I'd like to be able to get exp on the Ninja (whole reason for queuing as that class). And perhaps the ability to roll on gear for the class queued initially as well. Without this, the idea proposed has holes in it. When we queue as a role or class/job, we expect the rewards on that.

Switching class/job to finish a dungeon, and getting rewards on that instead makes it seem like it'd be best to leave and requeue, making the idea proposed a bit redundant. There has to be an incentive outside finishing the dungeon for posterity. Don't get me wrong, there's been times where I've wished I could do this, even outside the reward. Especially when running with a friend or two. And I could see players running roulette for tomestones doing this (as they're already max level and geared).