Does anyone know if the clear water sources along the
Labyrinth/Stillwater run (Three Canyon, Bonita Bend, Water Canyon) can
be counted on to have something in them in late September?

My GUESS would be, Water will almost certainly have water, so will
Anderson Bottom. 50/50 on there being water in the trail on the way up
to Upheaval Dome. Maybe 65/35. Last year in late Sept, there were
beautiful pools in Water Canyon, and the spring in Anderson Bottom was
cooking right along.

What do you mean by late Sept? I'm going Ruby to the Confluence
9/7-22, if you're starting after that I'll be happy to let you know.
Otherwise, the BLM people where you get your permit are a great source
of information, and certainly your shuttle people should be, also.