Pulling off the traps and snaking didn't help? I can see a P-trap leak being caused by snaking, it could certainly jar a fitting just enough. Do other fixtures in the room as well as your other rooms drain well? Any gurgling when you flush the toilet, or if you flush a toilet in another room does the water in the bowl of this toilet shimmer at all? Properly vented? All too often I'll see someone stuff a rag or wad up a bit of insulation to plug a drain stub-out during construction instead of using a proper plug. Several times they've disappeared...down the drain. Oops. Do these sinks have grates over the drain hole? Those can sometimes cause a little vacuum action as water leaves the bowl and that little vacuum can prevent proper draining. Do they have pop-up drain stoppers? Those can sometimes interfere as well. But not usually. Do the sinks have an overflow hole? Sorry for all the Q's. But 75 weeks? Wow.

Thank you SO much lazypup, brickeyee, busdriver, and everyone else for the clarifying pic, and the tips. Re: the profession-exaggeration, homebound, I kinda suspected it (since I get that from not only servicemen, but also society at large, all the time). Thanks for validating that, since misery loves company ;) In any case, I had done exactly that - in-person-summons... And he came last week and redid it though I'm not sure he followed all the steps listed in lazypup's pic. So far so good. The floor of the cabinet seems bone dry, and the finger-test tested dry as well. What's TP? Couldn't find it on google images.

Thanks, Vith. The goal is to gain counter space to one side of the existing sink cabinet, and I thought we might gain enough by shifting the sink cabinet as far to one side as the existing plumbing (inflows) allows. We may end up moving plumbing anyway, but we're on a tight budget so I was looking at less costly options. But if I understand correctly, you're saying the drain could still be in the center of the sink; is that right? I like the fact that an offset drain allows you to empty the strainer without removing, say, a large baking sheet from the sink, so I may opt for the offset drain anyway. I thought it might also simplify the under-sink plumbing as well.

What DavidR mentioned does happen. Also, the gaskets for drain lines are easy to leave not quite tight, winterizing a home allows unusual temps(as compared to normal living temps) and cold affects plastic pipes/gaskets more than metal. Rather than just watching, tighten the fittings(usually hand tight is fine) or hire a handyperson to check the drains(less expensive than a plumber).