I don't think the green is the best choice to float. Growing up in Kent, I was told that the Green isn't friendly to floaters/swimmers because it has an undertow that makes it dangerous. I could be misinformed though. Additionally, there are lots of areas where brush hangs over the bank, making it difficult to push off if the current took you toward the edge.
I've floated the Snoqualmie before, which is nice and relaxing. You can put in just after the falls. I think we got out at William F McCormick Park in Duvall, which made for kind of a long trip at 5 hours or so. It's been a few years though, so I could be mistaken.