Fixed! For anyone looking to do this, here's how. It would be better with capacitors like gryzynx said, but it works fine without them. Mine plays very similar to the radio quality, just without the usual static.
Remove the top and bottom case to your radio. You will need to find the brown and green wires at the top left of this photo, near the volume potentiometer. Ignore the rest of this photo, the wires on the pot don't have to be touched.
From underneath, use a small screwdriver to pull these wires out into the open. These are the left and right radio source wires.
Cut them in the center to give enough slack on each side and strip the ends off.
I used some info from this instructables, so when I talk about the jack pins, I'm referring to the picture given here:
http://www.instructables.com/id/Adding-Auxiliary-Input-for-an-mp3-player-to-an-O/step2/Background-Information/Before you do any of this, find where the wires will run out of the case and put your heat shrink on them.
Pins 3 and 4, the normalling contacts, need to be attached to each of the wires on the left coming from the radio source. Pins 2 and 5, the tip/ring contacts, need to be attached to each of the wires on the right going to the green board. Pins 2/3 and 4/5 must be on their respective color wires.
The ground wire from Pin 1, the sleeve contact, goes to the shield wire. This is the third wire next to the white and red ones underneath, as shown here.
Run the wires as you see fit. They can go out the back along with all the others. Put it all back together and you now have an aux input to play your mp3 player through!
Do this at your own risk. If you short something, you could screw up your radio. My connections weren't perfect and my radio only plays out one side now, but I don't care about the radio enough to go back and fix it. My iPod, however, plays great through all four speakers.
Edit:
I found the reason for the radio issue and will have to warn you to be VERY CAREFUL when soldering the pins on your jack. The plastic melts easily and will screw up the positioning of the contacts inside, ruining the normalling contacts for your radio and potentially rendering the jack useless. Mine is fixed now and everything functions perfectly.
A good idea for quality/safety is to run a capacitor on each of the source wires attached to pins 2 and 5. Use 0.05 - 1 microfarad, no more, no less, then solder and seal them properly.
If you prefer to attach it to your dash, you will need to drill a hole where it's going and use something to grind the inside thin enough to fit the nut on the other side. I used a dremel.
Here is my finished product.