leolaia your research is interesting but it doesn't change the fact that stauros is a word that makes no assumption of crosspiece unlike cross which does. that romans used execution methods that involve crosspieces as well as ones that didn't is a given.
But the original bible wording stauros which any historian will admit means stake/pale as you yourself admit makes no revelation of crosspiece it is a word more about the way Jesus died not the shape of his death instrument and that is the problem. You not only have to prove Jesus definitely died on a cross which is impossible but also that the writers intended a shape to be important.
All four writers of his death and references to it afterwards give no indication to it's shape at all it is completely in shadow biblically and should stay that way to be biblically true. I will say no more since I think my points are all well documented.