Yes, I thought about the basket or box idea. I thought it might by quite difficult to make a basket strong enough to hold a few tons of stone, so I went for the single stone idea, since we already know how we would raise it up. But, maybe a net made of knotted rope would suffice. I also thought of using water in a huge sort of goatskin (but probably made of cowhide).
The problem with the weighted rope is that as the rope sags the effective pulling power of the stone reduces, but equally as the big stone rises, the force needed to pull it upright reduces. It may be that these two forces can be balanced quite nicely, but I haven't done the maths yet. The danger of using a weighted basket is that as soon as the weight is sufficient to start moving the big stone, it might rapidly become too much. Using a block and gradually levering it back down while dismantling its tower would give us much better control of the big one.
Levering the monolith off the tower seems like we would then have to build some kind of lateral crib since the levers would very soon run out of reach. I considered that we could put a double layer of heavy timbers behind the stone (having levered it away from the tower) and then wedge these apart at the top, which would raise the monolith even further. Then a log dropped into the gap formed by the wedges would allow us to use levers off the tower with short props to the monolith. As we proceed, the log would descend further into the widening gab between the timbers preventing the monolith from falling back. If necessary, the monolith could be propped off the tower (or the ground) to allow the timbers to be repositioned. I know it sounds a bit hairy at the moment, but this is very much "seat of the pants" thinking. I'm sure as we thrash out the details it can be made to work. Perhaps the falling log idea would work well in conjunction with the weighted rope to allow the rope to be retensioned without risk of the monolith falling back.
