You'll all be thrilled to know that after three days of standing in a bathtub full of cat shit, I finally solved the problem.
Here is a list of things that did NOT fix the clog:
1 bottle of Drano Max Gel
2 bottles of Liquid-Plumr Foaming Pipe Snake

Several applications of Drain Out Crystal Clog Remover

Regular household plumbing snake (toilet auger)

Not so regular, specially purchased 25 foot plumbing snake

And before you start in on the "You shouldn't flush all those chemicals down the drain in such a short time, don't you know you have single-handedly ruined the environment and when we all die, we know just who to blame!!!" lecture, I will stop you right now and say that I've already heard it all from Man-friend, who stood behind me while I leaned into that bathtub full of shit and yelled at me-
"You need to learn to respect chemicals! They could kill you and Monkey-Butt and the entire world!!! What are you doing? Stop pouring chemicals down the drain, LET ME THINK ABOUT THIS PROBLEM, HOW CAN I SOLVE THE PROBLEM WHEN YOU KEEP POURING CHEMICALS DOWN THE DRAIN????!!!!"
And I was all "Dude, have you met my father? I would rather die a million chemically induced deaths than have him come fix this clog for me. There's no time to think, just hand me the f&*%ing Drano!"
As a matter of fact, I'm gonna add one more thing to the list of things that didn't fix the clog:
1 boyfriend

But...here is what did fix the clog:
2 bottles of Liquid Lightning Drain Opener

+
closing off all the drains and flushing two sinkfuls of water simultaneously towards the clog, causing it to burst out. (sorry no graphic for that one)
+ 1 bottle of cheap vodka

After all is said and done, I can say without a doubt that 1) Plumbers are underpaid and 2) I am now qualified to be a plumber.
And lest you think that I would never allow my son near another litter box, he was given that chore back immediately after I finished that bottle of vodka, had a quick shower, and my nerves were settled, except now he has to scoop it into a bag and carry it out to the trash can. Because no matter what, mommy is still lazy and would rather spend weeks standing in a bathtub of cat shit than clean the box regularly.