With some help, some advice and some elbow grease, I think I finally have the bathroom leak fixed.
A friend came over yesterday to look at our leak and came to the conclusion that the toilet probably had a hairline crack somewhere we couldn't see (or just naked to the eye). So, I ran out to Lowe's and picked up a new one. It's surprisingly easy to remove and install a toilet. The worst part was tightening the tank to the bowl. Getting a wrench back to tighten the bolts is next to impossible, but I finally worked it out.
Now we just have to fix all of the water damage and the damage we did to the surrounding dry wall trying to discover the problem. Yay.