I wish I could give a more meaningful update, but I was just promoted at my job and have been at work for 11 days straight now getting everything in order...basically trying to fulfill the duties of my previous position and my new position at the same time.
What I can say is that today I went to camping world to fill up on propane. While waiting, I asked the parts guy about the seal on the hand flusher since that has been mentioned here as a possible culprit. He said that no odor would come from a leaky seal, just water.
I don't know about the validity of that advice, but I have noticed that after releasing the flush handle, if you wait about a second after the water stops, one last spurt of water comes out. So maybe the seal is going bad after all, and maybe it's also letting odor out.
Also, I do not have an overflow hole in the toilet. It is my understanding that "newer" models don't have one.
Hopefully one day soon, I'll get to the bottom of this....