Here's a question I thought of related to this subject: Did the Romans execute their victims on the cross because it was a "pagan" symbol, or simply because it was highly effective in prolonging the torture? I'm guessing it was the latter, but maybe Leolaia or Narkissos would know the answer to this......
Cicero called the cross the "ultimate and extreme punishment for slaves (servitutis extremum summumque supplicium)" and "the cruelest and most disgusting penalty (crudelissimum taeterrimumque supplicium)" (In Verrem, 2.5.165, 169). I doubt they were aiming for any meaningful symbolism in an object that was so reviled. That's just how the apparatus was put together. In the fourth century BC the Phoenicians fought wars against Rome and the Romans encountered their Eastern form of mass execution involving the hoisting up of people up onto poles while still alive. The Romans started doing to same against the Phoenicians. But they had their own native form of punishment that the Phoenicians also imitated. Since ancient times, the Romans would execute some people by taking a patibulum from a doorway or a furca used in wagons and place it on the shoulders of a condemned slave and then force that slave to carry it throughout the city while whipping his body; then sometimes the slave would be whipped to death. Here are descriptions of this punishment pertaining to the time before the Punic Wars:
"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 his 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" (Dionysius of Halicarnassus, Antiquitates Romanae, 7.69.1-2; written in the first century BC).
"At an early hour of the day appointed for the games, before the show had begun, a certain householder had driven his slave, bearing a furca through the midst of the Circus, scourging the culprit as he went" (Livy, Historia Romana, 2.36.1; written in the first century BC)
"A certain man had handed over one of his slaves, with orders to scourge him through the Forum, and then put him to death. While they were executing this commission and tormenting the poor wretch, whose pain and suffering made him writhe and twist himself horribly, the sacred procession in honor of Jupiter chanced to come up behind....And it was a severe punishment for a slave who had committed a fault, if he was obliged to take a piece of wood with which they prop up the pole of a wagon, and carry it around through the neighborhood. For he who had been seen undergoing this punishment no longer had any credit in his own or neighboring households" (Plutarch, Coriolanus 24.4-5; written in the first century AD)
So basically the composite cross came into existence when these two forms of punishment were combined during the Punic Wars— a man would carry the patibulum with his arms tied to it through the city or Forum and then be hoisted up on a pole (often with his hands nailed to the patibulum and feet nailed to the pole).
It is not at all unusual that the crux would have a cross-like shape; it is such a basic geometric shape found throughout human artifacts. One only has to look through the world around us and see intersecting lines everywhere, just as triangles, circles, and squares can be seen everywhere (without intending any symbolic meaning by them). The early Christians pointed to examples like ploughshares, ship masts, trophies of war, the support for standards, etc., and yet none of these objects are made with the intention of having some symbolic meaning. It was rather the Christians who read symbolic meaning into the execution instrument; they were motivated to do so because it was hated by the pagan world around them whereas they saw it as the vehicle of their salvation, prophesied in scripture. The ubiquity of the shape in the world around them made them think that the crux was specially foreshadowed in nature and in invention. The expansion up and down and to the left and right was condusive to symbolism of the universality of the gospel and how it would spread throughout the whole earth, or that Christ's power is universal from the heights to the depths and embracing everything in between. All of this is drawing meaning from the geometry itself, not from any specific pagan religious uses of the symbol. If the latter were an influence later on, that would be a natural consequence of Christians looking for the cross everywhere in nature (with its use by man as a "preparation for the gospel"). But the cross was always the execution device that the pagans found disgusting (and on which many Christians were martyred); such use of symbolism had the obvious apologetic effect of going beyond the brutal reality to something more meaningful.
One thing I find interesting are the assumptions made by WT writers (and reniaa here). The use of intersecting lines as a symbol is not very well distinguished from the execution apparatus, as if the question of what Jesus' cross looked like has anything to do with the use of the cross-shape in (religious) symbology, as if pointing out that the geometric shape has symbolic uses in other religions somehow shows that Jesus could not have died on a cross. Jesus was not executed on a symbol; he was put to death on an instrument that typically had a geometry superficially similar to other geometries of intersecting lines. Because this is such a basic geometry (draw lines between the four corners of a square, what do you get?), it independently has symbolic uses in cultures all over the world; the swastika is a variant of it. The worldwide use of this geometry as a symbol doesn't point to some mythical "Babylonianish origin"; the ubiquity is plainly the result of the very basic nature of the shape.