Since you are open to all ideas, I think you should seriously consider a 16" 6.5 Grendel carbine. I just weighed mine, with magazine, ADM mount, and Vortex Viper PST 2.5-10x44 MRAD, and it is at
8.4 lbs, a joy to carry in the field. I don't even have the hunting lightweight barrel from AA either, just a medium-government contour stainless MLGS pipe. There are some Grendel hunters who have used Bushmaster Carbon fiber lowers, slickside or no Forward Assist uppers, double-fluted barrels, JP lo-mass carriers & buffers, with adjustable gas blocks, and gotten the weight down to around 5lbs
If you stick with the AR10-size action, your diet will include attacking the barrel first, getting one that is profiled much lighter. You won't want to go shorter than 16" for a hunting rig, unless you want to push the extremes at lower velocities and minimal shooter error for shot placement on game.
Then you will probably want to get a lo-mass operating system, with JP's captive spring.
In the end, the Grendel will let you do everything you want, coming well under the weight limits you're looking for, with a much milder-recoiling blaster that your family/kids can shoot and hunt with as well. The Grendel is also going to cost you the same as a 5.56 build, and mags are $15 a piece. I got my barrel/bolt combo for $269. You have 23+ factory loads, many of which are hunting loads with premium and affordable bullets, like the 130 Scirocco versus the 123gr Wolf SP, or the 130gr Nosler Accubond versus a 123gr SST. There is a nice line-up of Barnes TTSX, Nosler, Swift, Sierra, Hornady, and Berger to choose from for hunting with the factory loads, and well over 100 different projectiles to choose from if you hand-load.
I've owned 5 different AR10's, and the only one I can justify owning is my custom .260 Rem for serious long-range shooting, like 800-1200yds where it really shines. The Grendel ruined any more plans for AR10 carbine projects for me.