Your dryer cord almost certainly has a cord grip on it, the metal bits you see on the white part in this picture:
If you loosen the screws on that, you can move the position of the cord grip a little towards the plug to get a little more wire inside the dryer, then tighten them up again so the cord grip stays in that place. None of the wires should be strung taught, there should be some play in there.
The white stuff there is just a little extra protection for the cord jacket. If you have to move it far enough that it goes off that white stuff, wrap a few wraps of electrical tape around the black jacket under the cord grip for extra protection.
With a four-wire cord, that green-with-yellow-stripe jumper will not be connected to the neutral terminal with the white wire. That is for three wire cords. Remove that jumper, let it dangle, with a bit of electrical tape on it to cover the exposed metal. Or if you can do it, you could double up and land that and the green wire from the cord on that leftmost terminal.