It shouldn't take long for you to find a couple of cows. I live here in 65 (Teton Valley) and killed a bull on the river last year with my bow out of my kayak. The river corridor has very good numbers of moose, and though most of the land along the river is private, to date very little of it is posted, though that will be changing very soon I think give the rapid rate of land sales. In idaho you can hunt unposted/unmarked land without permission as long as it's uncultivated (read the regs carefully). I spoke with the local game warden about this last year just to be sure. The one thing I'm not sure of is if a landowner could have you busted for littering, etc for leaving a big gut pile/carcass on their property. Best moose numbers on the river are from South Bates road downstream to Packsaddle Road (400N). There is also good hunting on NF land in the Big Hole Mountains (west side of unit). I passed up several bulls up the South Fork of Horseshoe Canyon, but moose are scattered everywhere in the Big Holes - lots of ATV and cycle use there. There are also some moose on the BLM land in the SE part of the unit, but I'd hunt the river, especially since it makes it very easy to get one out via boat without killing yourself. Lots of rut action in Sept. for entertainment particularly in the mornings. Good luck