Just putting the "solution" here in case anyone else runs into this issue:
Audio probe told me IC1 was fine and that the noise was appearing in IC2 at Pin 1. Cut the chip out and soldered in a socket. Tried a bunch of different chips, all of them made noise except the OPA2134 and TL072/62.
The solution is "don't substitute a BJT op amp for a JFET op amp without using a socket." I had used a 5532 for IC2 thinking I was being clever because it's usually a little "cleaner" sounding -- that's a no go here. And apparently I just didn't notice the noise before. This is the second circuit I've run into this problem with recently. Sometimes you'll get a circuit that used a TL072 just because and a 4558 or 5532 will work just fine. This is not one of those cases. The OPA2134 sounds excellent here, though, a much more noticeable difference than elsewhere (probably just its better performance at higher voltages).
