The clay trap has been installed.
There wasn't enough room to simply come straight from the drain down to the clay trap, so I was forced to 90 out, then 90 down to the trap. That required the outlet to be routed over to the p-trap. I kept the p-trap in place so that if the clay trap is ever removed, it should be pretty easy to hook the sink back up with a piece of tail stock. I used schedule 40 1-1/2 PVC pipe due to the weight of the clay trap putting strain on the fixtures. I also put a small piece of pipe underneath the clay trap to give it some support. The support will need to be removed prior to dumping the trap and returned. The trap uses plastic bags, and I put them in the bottom of the trap underneath the bag that is in use. This reduces the chances of the bags being lost.
If the trap or plumbing for the trap ever needs to be removed, disconnect the p-trap and the 90 from the wall. This will allow the outlet to be removed, then the inlet can be disconnected from the sink by rotating the clay trap. You can also just cut things up and go wild, whatever your fancy.
Here is the before:
Here is the completed setup: