Use a self-signed ssl certificate in an iphone app
OK, I figured it out. I was sort of barking up the wrong tree.
The most important information I found was in Apple's documentation for Certificate, Key, and Trust Services Programming Guide, in particular, the "Tasks for iOS" page. That detailed how to extract the security identity from the .p12 file and how to add a trust exception.
The last piece of the puzzle was in ASIHTTPRequest's documentation on Client Certificate Support. By using the identity I extracted directly from the p12 file, I was able to pass that on to the request and get everything authenticated properly.
I hope this helps anyone else that has to implement a similar feature.