I checked with the cooler manufacturer (Igloo), the cooler is food-grade, but not designed for use with hot liquids. Whoops...
The flavor nearly disappears with cold conditioning, only so long as the keg is not jostled whatsoever (moving the keg seems to stir the flavor back up into the beer. I never did trim the liquid spouts in my kegs, and I usually don't crash my beers before they enter the serving keg, so there's always some trub stirred up if I have to move a full keg around). I think I'll let it settle until it can't be tasted, and then verrrry carefully transfer to a different keg.
I did at first suspect that the plasticy taste might be caused by grain husks mashed thinly/hotly/lengthily, especially since the flavor is most noticable in beers with roasted or toasted malts. I am confident that the cooler is the culprit, because I detected a revoltingly large amount of the same flavor in plain water which had been left to soak in the cooler at 180 degrees for 5-10 minutes. I think I'll try the same experiment, but with the manifold taken out, to narrow it down.
I have heard of chlorophenols described as "plasticy" (and especially as "band-aidy"). I have encountered an infection-created phenol flavor before (probably from a Brett infection, due to the horse flavors also present). It's not what I am tasting today, and there are no other infection flavors present, so I doubt there is an infection problem. I'm not sure if I've tasted chlorophenols, so I can't rule them out, but I think it's safe to finger the cooler as the source.