Re: .223 in an ar10
well, if you went with a standard AR15 bolt, you would need to have a custome carrier made so a custome diameter inside could be made to match the AR15 bolt. You would need to have a custom barrel extension made that would have the outside the size of a standard 308 AR extension and have the inside design for a standard AR15 bolt. Gas port size would have to be adjusted also since your moving a lot more mass of that AR10 style carrier. you are also going to need to create a custom insert for the magazines, or just create magazines, maybe modifing 5.56 mags buy cutting and extending the front, but then you need a mag well adaptor to allow the mag to be held in place.
Another would would be to have a custom 308 sized bolt made to hold a 5.56 case, along with a matching custom extractor. this would allow a standard barrel extension and a standard carrier. but you will still need to tweak and play with the gas system and have some sort of custom made mag.
I am sure it can be done.....question is.....do you have enough money you are willing to spend to pay for it? with design work and the production of a couple "one off" parts, my guess is it is not going to be just a couple hundred dollars.