Here's a point I haven't seen mentioned (though I admittedly have only scanned the thread).
Post hole diggers weren't exactly commonplace back in the first century. And despite the belief that we're talking about some sort of primitive society, these people weren't stupid. It seems to me that it would be incredibly practical to have your upright poles permanently established in the ground in order to avoid stability issues rather than dig a new hole and mount a new pole for every single criminal executed. They may have even been living trees or the trunks of trees that had been trimmed and cut at an appropriate height. What did Jesus and others executed in those days carry to the location then?
I think the answer is obvious: the cross bar their arms would be nailed to.