The sub box will only support up to a 8 inch subwoofer. There's not enough space to accommodate a 13 inch sub. I personally wouldn't recommend a 13 inch unless you plan on doing some customization that will require sacrificing space and looks.
My plan is to install the Alpine SWR-843D 8 inch unit. Also, you may want to look into the dimension of the JL amp. It may not fit. The stock amp is small and mounted vertically behind the glove compartment.