"Presumably the top end would be supported by the tower".
I wonder if you're thinking that I'm thinking the timber would be on the near (left on Gordon's model) side of the hole. I was thinking of it being in the hole and slightly leaning towards the right, i.e. propped against the right hand lip of the hole. So the earth would take much of the impact. Plus, additional buttressing for it at it's top end, if needed.
I guess in my layman's terms I was thinking if we were allowed to have a really deep tapering hole then it would be really easy to get the stone upright in it, but since we are only allowed a shallow hole why not effectively lengthen the hole's far side, upwards and at a slightly widening angle, using a tall piece of timber (or several). So far as the stone knows, it's now being tipped into a tapering deep hole and if the timbers don't break it has zero choice but to end up pretty upright.
I may have misunderstood you though in which case sorry about banging on about it.