Quick update on this. Now that I've further torn into my car, I don't believe mildew was the issue. I've also decided that the black color that was in the pad (sorry, I deleted the images) was tar from the sound proofing.
After I removed my carpet, the smell did diminish but was not completely eliminated. When I dismantled the dash to remove the wood bows, I discovered a lot of mouse droppings. I vacuumed up all the droppings and blew out the areas I couldn't reach with compressed air. I also cleaned all surfaces I could get to. Voilla! I can no longer detect the obnoxious odor.