With some help from the GStreamer developers I found the answer.... don't use version 0.10.36. :)
Basically the ability to build static plugin libraries was added/fixed in later versions. To get it to work in 0.10.36, I've had to back port changes from the GStreamer SDK and GStreamer 1.x into 0.10.36. Things are still a work in progress, but I am able to build libgstcoreelements.
a and statically link with it. If I wasn't already building a modified version of 0.10.36, I probably would have just used the SDK.
Update
I created static versions of all of the libraries I'm using. My GStreamer library is now a bit of a hybrid between 0.10.36, the SDK, and 1.2.2, but it works. I wouldn't recommend this solution for anyone though. Use the SDK or version 1.x.