The devil is in the details. You've pretty well covered the ground, but you left out a thing that is important for function of the gas system. The different gas tube lengths have different volumes, and they admit gas to those volumes at considerable pressure differential to achieve the same level of bolt manipulation. I'll put this in analogy form, though such is always suspect. If these were springs, the pistol gas tube would be a very short, very stiff spring. The carbine length is a bit longer, and not quite so stiff. The progression continues with the mid-length and rifle versions of the tube. The math gets very interesting when you start messing with gas flow and friction in these small vessels, but it is available in most of the physics books these days if you need to go deeper than this.