I've done many, many multi-day river trips in multiple countries. I've done them in hardshell kayaks, inflatable kayaks, and rafts. I am lucky enough to get to go on a 28 day Grand Canyon trip next month. I also used to guide in northern MN in the BWCA out of canoes...not saying this to brag, but just to give a bit of credibility.
In an ideal world, for a 7 day trip with 2 people, you would have 14-16' oar frame raft. If that's not realistic, I'd start looking toward inflatable kayaks. I own a few and I use them all the time for overnight fishing trips on the Deshutes, day trips on the Klickitat...I have used them for duck hunting a few times but never big game. I like IK's because they are very user friendly, you can get in and out quickly, they are very stable, and you can pile loads of gear in them.
I personally use IKs from a local company, Aquaglide. Check out their Blackfoot XL model. I also use their Klickitat 2 when there is whitewater involved, although I've taken the Blackfoot down some of the II-III on the Deschutes...wouldn't necessarily recommend it.
I'm also looking to do a float mule deer hunt in the next few years! I actually posted about it a month or so ago. I hope you can get everything sorted out!