I have some more observations from the computer model. There's some bad news and some good news for you practical types (I'm a practical type too, but I like to get the theory worked out first).
The bad news is that the rotational inertia of the block depends on the square of its length. That means that a 32 foot block will rotate 4 times slower than a 16 foot block, but will build up 4 times the momentum. I suspect this is what Gordon meant when he said that the large stone was more "predictable". Anyway, you can't just scale up a small model.
The good news is that no part of the motion is dependent on the weight of the block. There is a small dependency on the square of the width as well as the length, but as long as the length is much more than the width this effect is negligible. For example if the length to width ratio is 10:1, the width contributes only 1% to the overall inertia. So you could use a 32 foot piece of timber or a scaffolding pole as a model for a 32 foot stone.
There is a considerable sideways force on the tower. This arises because the rotational acceleration of the stone is being created by the reaction force of the tower (to every action there is an equal and opposite reaction). This force is always perpendicular to the surface of the stone at the point of contact so as the stone rotates so does the force. My model will calculate how big this is and at what angle it reaches its peak value, but at a guess I would say that it will be a large fraction of the stone's weight, perhaps as high as a quarter. The tower needs to be designed to withstand this force. If it's constructed with logs I would suggest that the pivot log is made extra long so that it projects beyond the sides of the tower. Long bracing logs can then be attached to it and anchored into the ground behind the tower to resist the thrust.
Gordon, what is your plan for building the towers. I envisage that a pair of logs will be placed each side of the block at one end and used to lever the block up until a transverse pair of logs can be slipped in ontop of the first pair to take the weight of the stone. The process will then be repeated at the other end. The next lift will require two more side logs to be placed on top of the transverse pair and used to lever the block up for the next transverse pair and so on. This means that the overall lift needs to be at least two log diameters. Using 6" logs would therefore need a lift of 1 foot. Do you envisage any way of fastening the logs together to increase stability (e.g. rope lashing)?
One point that toubles me greatly is the release mechanism for the A frame. I can think of two disasterous scenarios. Firstly, what if one of the poles slid away cleanly, but the other dug into the ground? This would deflect the block sideways and it would miss the hole. Secondly, what if the A frame collapses on to the hole? The block would probably smash the timber as it hit, but it might be deflected enough so that it fails to "plant" correctly. I would prefer a release mechanism that caused the support to topple outwards away from the stone. One idea is to have a lever on top of the A frame with its long end projecting away from the stone. A rope attached to this lever could be run up and over the stone. When the rope is pulled (from the "safe" side of the stone), the lever moves upwards and prises the A frame out from under the stone. The A frame would then collapse out away from the path of the falling stone.