Like today, the Romans were very careful and precise about how they performed legal- especially 'visible'- executions. And how they carried out efficient method.
Although it may not seem as exciting, the 'pole' used to execute Jesus was a standard device, that required no crossbeam. The expense in labor and material, the medical impossibilities and impracticality, merely reinforced the procedural issues.
Then, also, as has been noted (above), the Original Scriptures state clearly that Jesus died on a "stauros"- "stake" or "pole"- not on a cross or crossbeam, which was adopted as a religious symbol of Christendom, centuries after Christ, due to Roman imperial influence.
The cross was actually an instrument of Roman military muster, and is associated with a variety of popular, unchristian uses.
A Roman execution pole, alone, would've been quite heavy, especially for a beaten man to to carry. A crossbeam, would've added a significant amount of weight to the struggle, of course. And would then require ropes and possibly pedestals, to make feasible, rather than relying on the duel placement of tendons, that- together- not individually- could support the load of a human body; which is one reason that the Romans performed executions with solitary poles.
Offhand, I'd rely on the common view, which is about a 1/2 mile.
However, there are other considerations, such as the detail of the area that was traversed, and the location of detention, in relation to the site of execution.
It was certainly a rugged experience, one can easily imagine having to drag a heavy pole of timber, without being injured by the process, alone.