This was a subject I researched exhaustively years ago.
1) The Romans did crucify prisoners and slaves in the first century with a two-beamed cross and the words crux and stauros did denote such an execution instrument (cf. Plautus, Lucian, Artemidorus, Seneca, Tacitus). The Society's repeated claim that Livy used crux to only denote impalement is without merit; Livy never gave any indication of the shape of the crosses he mentioned. The claim that Lucian used anastaroo to denote impalement in his play on Prometheus is also contradicted by the evidence. By claiming that crux and stauros did not mean "cross" until the third century, the Society is intentionally distorting and hiding the facts.
2) The Gospel accounts assume a two-beamed cross, especially in the motif of Jesus or Simon of Cyrene carrying the cross on the way to Golgotha (cf. John 19:17) which is nothing other than the widely-attested practice of patibulum-bearing (the patibulum was the crossbeam). This practice pre-existed the invention of crucifixion as a method to torture disobediant slaves (cf. Dionysius of Halicarnassus, Plutarch) and was widely adopted as a prelude to crucifixion (cf. Plautus, Plutarch, Artemidorus, Chariton). The Society would instead require Jesus or Simon to carry a pole to Golgotha (actually pictured in the Greatest Man Who Ever Lived book (1991, chapter 124), which is utterly without any historical support and ignores the copious evidence of patibulum-bearing. John 19:17 and the synoptic tradition of Simon of Cyrene are fatal to the Society's crux simplex theory. The traditional Christian picture of Jesus carrying the whole cross over one of his shoulders (seen in the Passion of the Christ movie) is also unhistorical....what the Romans apparently did was have the prisoner stretch out his hands, nail or tie the hands to the crossbeam, and then having him bear the beam over his back or chest throughout the city to the stationary stipes (vertical beam), and then hoist him up to the cross. This practice is also alluded to in John 21:18-19 which also assumes a two-beamed cross. Details in John 20:25 and Matthew 27:37 are also best explained by assuming a two-beamed cross.
3) The use of the word xylon "tree, wood" in Acts 5:30; 10:39; 13:29, Galatians 3:13, and 1 Peter 2:24 does not indicate the kind of stauros Jesus died on, only that the Bible writers understood Roman crucifixion in terms of the law in Deuteronomy 21:23-23. Other Jewish writers referred to Roman crucifixion in the same manner (including the Dead Sea Scrolls, Philo, Josephus), and Roman writers also referred to Roman crosses metaphorically as "trees" (cf. Seneca).
4) There was a strong tradition in late first century and second century Christianity (cf. Barnabas, Justin Martyr, Odes of Solomon, Irenaeus, etc.) that repeatedly looked for prophecies and prefigurings of the two-beamed cross of Jesus in the OT, and described the stretching out of the hands from side to side as a sign of Jesus' cross.
