I am the Jake of home ownership. [Update 2] I think I fixed it.

Came down to swap over the laundry to find both utility sinks overflowing with grey water. Oh yeahhhhhh. Ran the kitchen sink and bathroom sinks successfully, so the immediate drain beneath the utility sink seems to be the culprit. Also confirmed the main sewer line out is fine. The problem is everything beneath the Y-pipe is glued, then galvanized further down. Scooped out 20 gallons of water with a damn plastic pint pitcher.

Please send your worthless thoughts and prayers that this power snake will work.

[Update 8:25pm]

Wow, power snakes are both fun AND frustrating. Anyway, ran the drill for a long long long while, put everything back together. Run the sink water. It drained but incredibly slowly. Take everything apart again. Re-snake. Snake gets deeper. Snake gets stuck. Spend 20 minutes getting snake out. Put everything back together again. Run sink water again. It drains... okay.

Moment of truth: I run the washer again. Sink fills up halfway. Barely draining. I pause the machine and say “fuck” about six times. Sink slowly drains. I resume the cycle... Second gray water discharge: drains a little faster. Third discharge minutes later: drains at almost acceptable-ish speeds. There is progress... I think. There’s one last massive discharge before the spin cycle. Let’s hope.

[ Update 2]

Last discharge drained just like it used it to. No pooling. Wife brought me wings. I’m done.