It has been suggested by more than one person that perhaps our bathroom is possessed by malign spirits and that is the reason why we're having so many problems with our remodeling project. So, I performed an exorcism of sorts this evening. Brian's skeptical, but we'll see how things go from now on. I'll keep you posted.
Already, I see an improvement. I wouldn't say we worked in the bathroom this evening, but we did disconnect the toilet to see what the problem was. The job was surprisingly easy (it doesn't take long to disconnect a toilet) and we didn't make a mess because we sucked all of the water out of the toilet with a shop vac before attempting anything. Yesterday's problem turned out to be a simple misalignment of the wax ring. I think we might try one of the new non-wax gaskets for our next attempt. That way, if there are any issues, you can make adjustments rather than run to Lowe's for yet another wax ring.
***Clutch, "Burning Beard", Robot Hive/Exodus