Thank you to everyone on this thread for your patience and generosity with your expertise. With your help, I not only learned a great deal about segmentation and addressing, as well as how to use the Bochs debugger, but I also was able to finally get my exception handler to fire.
I really appreciate everyone stepping in to help me out. The purpose of my OS is to find and document more of the hurdles for the amateur who might know C and OS principles but who has never had to write for the x86 at such a low level. This will definitely be a subject for my documentation pages!