API is cheap for a variety of reasons, the biggest is that almost NO ranges allow their use. 50 BMG API start fires and make them big very fast.
Surplus bullets are not very accurate because they're mass produced. Plus they only have to meet the government standard of about 2-3 MOA. The brass is the same as far as government standards go. Then throw in the loose chamber of a machine-gun that only has to put so many rounds into a beaten zone.
There are companies that make bullets that are cheaper than AMAX, look at Lehigh and Hawk bullets. Those will keep you at MOA or better all day long and ranges won't have a problem with you using them.
Brass is another issue, brass that's been fired in an M2 and stretched out and beaten up wouldn't be my first choice. Either start out with new brass or once fired that's been shot out of a bolt gun.
New powder will be best for match ammo, you can use new or pull down for reloads. There are match primers out there, RWS makes some, not sure if any American company does. You can check Ten-X to see if they have any or pass along info on where to get some.
The only company that made match grade ball ammo was IMI. If Anthena (PPI) would've got the contract for .50 ammo, it would've been another one. I don't think IMI makes it any longer, the couple of boxes I have are for the collection.
As for loading your own and getting MOA, that's very hard. You have to find ball or better yet AP that's in very good condition to start. Brass that's the same and then prep it to make it better than standard. To keep this short, match prep everything!
Even after doing all of this, your best will be MOA or 1.5 MOA. Which isn't bad for surplus components. But a lot of work for what the end result is compared to starting out with match components.