Restricting oneself to the most literal of meanings is often wrong in any language. We cannot simply say "what does this word mean at its root?" We must go on to ask "how was this word used in this verse?"
That the preferred form for a Roman cross was indeed a vertical stake with a crosspiece is well established in history. Stauros could mean "cross" more than 100 years before Jesus. There are several lines of evidence which show that Jesus died on a cross and not a pole.
While one famous argument against the cross is that the description of the cross isn't used for several hundred years after Christ, specifically that Constantine introduced it, Justin Martyr describes the cross several times in his Apologies (ca AD 155):
And again the same prophet Isaiah, being inspired by the prophetic Spirit, said, "I have spread out my hands to a disobedient and gainsaying people, to those who walk in a way that is not good. They now ask of me judgment, and dare to draw near to God." And again in other words, through another prophet, He says, "They pierced My hands and My feet, and for My vesture they cast lots." And indeed David, the king and prophet, who uttered these things, suffered none of them; but Jesus Christ stretched forth His hands, being crucified by the Jews speaking against Him, and denying that He was the Christ. - First Apology, Chapter XXXV
Had Justin believe Jesus died on a stake, he would not have linked these verses together. If he thought Jesus had died upon a stake, he would have described it as Jesus stretched up his hands not stretched them out. Even before Justin, The Epistle of Barnabas had reasoned the same way (that his hands were stretched out to the side in fulfillment of prophecy). However, he is even more explicit in his second apology.
"God does not permit the lamb of the passover to be sacrificed in any other place than where His name was named; knowing that the days will come, after the suffering of Christ, when even the place in Jerusalem shall be given over to your enemies, and all the offerings, in short, shall cease; and that lamb which was commanded to be wholly roasted was a symbol of the suffering of the cross which Christ would undergo. For the lamb, which is roasted, is roasted and dressed up in the form of the cross. For one spit is transfixed right through from the lower parts up to the head, and one across the back, to which are attached the legs of the lamb." - Second Apology, Chapter XL
Further, in chapter LX, he compares the instrument of crucifixion to the sail on a Roman boat (which had a cross piece), to a person with their hands stretched to the side, and to a vexilla (the Roman standard used to carry the banner in procession. It had an upright piece and a cross piece to which the banner was attached).
Another writer, Tertullian clearly identifies the use of a cross in his writings dating from A.D. 190-220. He also shows that the difference in a cross and stake was expressible.
"You hang Christians on crosses (crucibus) and stakes (stipitibus); what idol is there but is first moulded in clay, hung on a cross and stake (cruci et stipiti)? It is on a patibulum that the body of your god is first dedicated" (Apologeticus, 12.3).
"For this same letter TAU of the Greeks, which is our T, has the appearance of the cross (crucis)" (Apologeticus, 3.23.6)
Ireneaus (ca AD 170) wrote that the implement of Jesus' death had five ends: two longitudinal, two latitudinal and a fifth to support the weight of the victim (Adversus Haereses, II, 24, 4). Both latitude and longitude shows that the implement was a cross and not a stake.
The amount of time Jesus and the others took to die also indicates a cross. The goal of crucifixion was to publicly shame the convicted and serve as a warning for others. Death on a cross takes a long time. However, death on a stake is much faster (examinations of WWII experiments show that death on a stake was finished in an hour at most). However, Pilate marveled that Jesus was already dead (Mark 15:44). However, the other two convicts were not and their legs were broken to speed the process (John 19:31,32). Had it been a stake, that would not be necessary.
Historically, it is known that the Romans used crosses with cross pieces in the first century. The JAMA - Journal of the American Medical Association, March 21, 1986, Volume 255; Copyright 1986, American Medical Association states:
Although archaeological and historical evidence strongly indicates that the low Tau cross was preferred by the Romans in Palestine at the time of Christ, crucifixion practices often varied in a given geographic region and in accordance with the imagination of the executioners, and the Latin cross and other forms also may have been used.
Primary source material also shows that the crosspiece was used by the Romans prior to Christ. Dionysius of Halicarnassus says,
"A Roman citizen of no obscure station, having ordered one of his slaves to be put to death, delivered him to his fellow-slaves to be led away, and in order that his punishment might be witnessed by all, directed them to drag him through the Forum and every other conspicuous part of the city as they whipped him, and that he should go ahead of the procession which the Romans were at the time conducting in honour of the god. The men ordered to lead the slave to his punishment, having stretched out both hands and fastened them to a piece of wood (tas kheiras apoteinantes amphoteras kai xuló prosdésantes) which extended across his chest and shoulders as far as his wrists, followed him, tearing his naked body with whips" (Roman Antiquities, 7.69.1-2)."
Before Christ, crosses with crosspieces were known, used, and even preferred by Roman executioners