Welcome from New Mexico, from an old Kansas boy. I hope you have a place locally to stretch the legs of that M&P-10, last time I was in Hutch we had to drive about 25 miles to get to a range where we could shoot out to 100 yds!
Also, you are not building an AR-10! You are building a DPMS based AR 308. The AR-10 is made by Armalite and some parts are different than the DPMS based rifles. We try to point that out to newbies because it CAN make a difference if you have issues with function of the rifle.
Several of us have done builds on Matrix receiver sets. The barrels shouldn't be a problem, both platforms use the same barrel, just match the bolt to the barrel.