If Armalite makes an upper that will fit their AR-10 lower, and they will tell you, then yes you could do that. You will have to use cartridges that are designed for the AR-10 magazine. Because of the way that the upper is cut, you can only use Armalite AR-10 uppers with their lowers (in whatever caliber).
For an all around hunting HD weapon, get the 16" flattop carbine. It will spit them darn good out to 400 easily, and it is still short enough for the home/vehicle.
If you are looking at more of an AR-15, then I would suggest that you look at getting a AR-15 in .223 for home, and then getting a 6.5/6.8 upper for it to go hunting.
FWIW, I have the AR-15 and an AR-10. I love my 10 and it puts an 15 to shame in size.. I may make a different choice now, and get the 6.5/6.8 upper instead, but at the time I had lots of .308 supplies, and adding another caliber just offended me.