Have a serious look at the Natashquan on Quebec's north shore, it fits your requirements.
It is a fly in trip, the rapids (Class II-IV) are concentrated in the upper section of abut 100km, the 300km second section runs through a wide valley and is more of a float trip with just some swift water sections but always a strong current. The upper section is very rugged with plenty of exposed rock, once you cross the border from Labrador to Quebec you are into a lot of sand, if the levels are right beautiful sandy beaches to camp on. Scenic value in both sections is very high.
I paddled the river in 2014 (2 solo boats) but we accessed it via an overland route that took half of the 36 days just to reach Lac Natashquan. Water levels on the only gauge (which is a long way south) were at 400cms falling to 200cms when we finished. I would not want to try the upper section at too much higher level, while the water was obviously low the fabulous beach camping on the lower section compensated. I only recall grinding on a few sand bars and a lot of easy drifting, 300cms would have been better!
The is also an East branch, it has not been paddled often so not too much info is available.
Guide available here:
http://www.cartespleinair.org/Canot/07/ ... er2013.pdf