M_P,

Water levels do make a big difference. Up or downstream. Spring unless it's a dry year, the flow can be fast an furious. I believe in the trip reports archives, Snow Dog went downstream in high water conditions. His pics tell the story.

I went one spring, with low water levels. Completely different paddle.
I actually had to paddle more than I thought I would in the narrow sections.  In low water level, Tanner Lk is basically just like any other lake, the wind direction/speed might be more than any current at the time? I would think with a decent start, you should be able to get to Twin falls in a days paddle easily, unless the water level is high and the portages flooded out.

I'm guessing in Sept the levels will be down, unless there's a lot of rain late in the summer.

I can't speak to a " can't miss campsite", but there are sites along the way, and dependiong on conditions, how far you want to go, you might find your own gem.