A winner is me. I got it.
Yeah, I let it sit in there a while. Wife and I had a scheduled vacation and then she had us spend last night putting together a toy kitchenette for our daughter that had arrived. Not a big deal, we've got other bathrooms.
Tried to shop vac the thing out. Nope. Gave up, took the whole toilet off, laid it on its side, shoved my super industrial snake up its backside and gave it a go. After pushing the entire toilet two feet across the floor trying to clear the blockage it bumped up against the wall, which was nice. No more chasing the toilet.
Couldn't get enough force behind it to clear it out. So, took the tank off, hauled it outside onto the deck, flipped it upside down, shoved my apparatus up there and went beast on it. My daughter (20 mos. old) cried a bit seeing daddy grunting and bouncing a toilet around the deck.
But, I got the bugger out, put the toilet back in place, and cleaned the whole mess up.