That in the red circle is the clean out plug that I've been trying to remove. Sorry about the crappy (no pun intended) contrast. Everything in there is pretty much rust orange, now that we've washed most of the other color away.
I am led to believe that wherever this clog actually is, it's quite a ways away from this drain. If we don't use any water for a while, like overnight, in the morning we can flush or brush our teeth (if we do it quick) and we're fine. Eventually, the water draining will hit that clog and back up, but it usually takes a couple minutes (or a few toilet flushes right in a row) for that to happen. It's not immediate. I'm really hoping it's not roots, but I'm beginning to think that may be what we're dealing with considering all the symptoms we're seeing and hearing.