Thanks Mike. I wound up replacing my closet auger with a new one that cost less than 8 and that did the trick. The old auger had a kink in the coil and apparently that was misdirecting it. It was stick deodorant that my daughter flushed down when no one was watching her. It was partially plugged and not siphoning well. I hit something with that new auger and started turning it and little pieces of the deodorant came up into the bowl. I didn't recover much of it but I'm hoping the rest just flushed down because it is siphoning normally now. The old bent auger must have just bypassed the clog because it went through the siphon easily.
It is still annoying that a standard flange plunger won't seal around the hole. If you happen to pass one in a store, look into the bowl you will see what I am talking about.