The Section of the Middle Fork from Schafer Meadows to Bear Creek is more treacherous than the South Fork and has sections of class II- IV whitewater and log jams do occur. We do not recommend floating this section at high water and portaging of the class IV sections is recommended. You can hike into Schafer or fly into the landing strip at Schafer Meadows. American Whitewater offers a description of this section. While no permits are required there are restrictions regarding waste and camping on this section of the river please see this Forest Service PDF for details.
The ultimate way to see the Bob Marshall Wilderness is traveling down the South fork of the Flathead. The section of the river from Big Prairie to above Mid Creek is considered class II water and is 31 miles of wilderness river water. American Whitewater offers a description of this section. You can access the South Fork via backpacking, backpacking and creeking, or horse back. Ryan Jordan offers a great description and video of a packrafting trip on the South Fork:
There is an abundance of mountain lakes in Montana! Consider backpacking into a lake with a packraft and being able to lounge on a raft fishing your way around the lake. Glacier National Park is packraft legal!