Dude, keep that ammo. You're not going to do better than Lake City USGI in bandoliers. 16000 rounds isn't THAT much. Look at it this way, you can set aside a couple of thousand rounds for a SHTF stash and still have enough to practice with for the next 4 or 5 years.
Besides, it's your family heritage. Your Grandfather obviously believed in firearms and preparedness (No one keeps 16000 rounds of USGI 5.56 on hand for deer season). Keep it in the family, use that ammo to develop and build your shooting skills as a way of honoring him and keeping his memory. Don't just try and cash in on it.
Seriously, it's your family legacy. Your Grandfather must have been a pretty cool guy. Never sell the family treasures, and if 16000 rounds of USGI 5.56 isn't a treasure, I don't know what is.