Glad we called the Roto Rooter guy – he was nice, professional, and his machine had a long enough attachment to reach the clog, which I’m not sure the rented snake would have had. He rooted the thing all the way to the main, so I’m sure the drain is clear. We have some roots in the drain, which is bad, bad news, but hopefully, not serious enough that we can put it off for a bit. Worrisome, but not fatal.
Now, on the way to Home Depot to get a tank attachment kit, and a 4″ to 4″ coupler, as well as something to put into the cleanout to close it up, at least temporarily. Lovely. At last, though, that issue is gone.