Realistically, only Armalite makes compatible uppers for their lowers. Except maybe some older Noveske uppers. They used to make their stuff to the Armalite spec. But that was years ago, and finding a unicorn would probably be easier. Keep in mind that a stripped upper from Armalite (or other parts places) will run around 300 bucks. The BCG will be another 250. So you're already over half way to that 800. Then you add a barrel, gas block, gas tube, charging handle, sights......blah, blah, blah.
Really, 800 to get a functioning AR-10 upper isn't really that bad.
Building Armalite rifles/carbines isn't the cheapest way to make things happen. Go ahead.....ask me how I know that. I've got (a few) of them. Armalite and cheap don't go hand in hand.