UPDATE!!!!
Broncovan and I went out to the range this morning and set out to determine if a RRA LAR-8 upper would fit and function on a Bushmaster BAR-10 lower.... Here is what we found.
First thing we disassembled the BCG and found that my buddy apparently does not know how to clean a rifle!

We began by looking at the the BCG and found that they appeared visually identical. (note: we did not measure them, just visual examination.) I then noticed that the Bushmaster bolt had a shorter length extractor, which did not extend into the carrier. The RRA had a longer extractor that did extend into the carrier, similar to a standard AR-15.
We then removed the bolts from the carriers and found that the rear neck of the Bushmaster bolt had broken off and was flopping around on the firing pin. The bolt was so dirty that we actually thought it was a completely different bolt design at first. Then we realized it was broken. We then test fitted the Bushmaster bolt into the RRA carrier and vice verse. They did not fit. Figured that they may of had a slightly different body diameter or had something to do with the length of extractor.
Next we looked at the feed ramps and upper receiver internals. Everything there appeared the same. So we slapped the RRA bcg into the Bushmaster and loaded it up. It fed a round just fine and completely seated it in the chamber, I did a brass check and slapped the forward assist just for grins (all though it was not needed).
Then I clicked the safety to FIRE and bang, bang, bang. Three rounds perfect. So a RRA BCG will function in a Bushmaster upper receiver.
We then swapped out the Bushmaster upper with Broncovan's RRA. After getting the the front pin put in and putting the RRA bcg into the RRA upper, I closed the upper down onto the lower and it was as tight fitting as the Bushmaster. Both pins fit perfect and the upper and lower mated together like they had come from the factory together.
The combo fired perfectly with two different types of ammo. No failures, jams, hick ups or jerks.
We did not do an extensive firing test as we were primarily wanting to see if they fit and fired together, which they did.
The one thing that we did not check was the Bushamster bcg in the RRA upper due to my buddies broken bolt.
All in all, I would say that the parts are interchangeable, with the exception of the bolts.
Another interesting thing we noticed was the barrel nut on the Bushmaster. It actually had two rows of teeth on it. The standard handguards mounted up to the first row and the second was taller and held the gas tube in place. We could only assume that they did this so that they could use standard HG's they had at the factory, but they needed the extra (taller) row to help support the gastube. Broncovan's RRA had a free float tube so we could not compare barrel nuts.
I apologize, I did not take photos, I thought of it after the fact.
I hope that this helps those of you out there that have had questions about AR-10 parts.