Update - I finally got my hands on an OEM Aux cable and, lo and behold, it works! So the two aftermarket cables I tried before were obviously just garbage. Just another lesson to stick with OEM if you can.

Anyway, now all I need to do is figure out how to mount the Aux input into the little compartment below the stereo. The installation instructions only show you how to install it in the glove box, which seems like a pretty stupid location to me.