Dude, you can still pogo it. Find something wooden with a sharp corner. Basically, you're going to run the upper along the corner until the charging handle latch contacts the wood and yanks the bolt open. Takes more coordination than the traditional pogo, but it does work. I have to use that method once on someone's AR at a class - the instructor would not allow the pogo method because if it were to fire, he could not account for the bullet. Doing it on a 4x4 post, the barrel was pointed into the berm. Just make sure not to put too much lateral force into it or you run the risk of snapping the charging handle (I'm not sure how robust the ar10 handles are). Also, wood can leave marks on the rifle, so if you're going to be upset by potential marks, then don't try it.
Also, I can't believe that you can't put it back together. Can't you tuck the carrier in and then rock the front down onto the lower and then pin it all back up? If it'll come apart, it'll go back together. Don't pin the front first, that way you can use the front to back leeway to slide the carrier a little way into the buffer tube.
