My turn to pile on. Brother John, the engineers on this board are here to help you, but it would have helped if you were more direct.
Like this: is your station WBWC? If so, your "large metropolitan market" -- Cleveland -- is chock-full of insanely-qualified engineers.
Speaking of which, I see that the WBWC website has a person listed as Chief Engineer. This is not the place to get into "I said / he said", but assuming this is your station, have you worked with him regarding this problem? Again, this is not really the place to answer that question... but it is to ask it.
I've worked with volunteer-run stations that broadcast a variety of programming, and I understand that it may be hard to cut through the noise to get attention focused towards a hard-to-hear or hard-to-track issue. What the posters here are suggesting is for you to follow a more "scientific" approach of observation and elimination in order to help your engineer find the problem.
I will give you one "non-invasive" test that you can run: find a fixed receive location no more than about a mile from your transmitter, preferably one with a clear view to the tower (i.e. not in the middle of a mall or other building). A quick search shows a bunch of restaurants surrounding the tower site that should work nicely, and I assume many have lots of glass and handy outlets. Remember the goal is repeatability.
To this location, bring as many FM stereo radios as you can muster. Bring at least one good set of headphones such as a pair of Sony MDR7506's. The problem may not be the hearing of us "old people" (ahem!), but that 12 kHz ain't so easy to replicate via cheap headphones or car speakers. Make sure you are in a location of excellent signal.
Find a time when both WBWC and another station have silent passages, such as between programs. WCPN looks like a good candidate, since they are in talk programming most of the day. I assume you can find a cooperative WBWC DJ to give you some periods of silence.
Now, when both WBWC and the reference station (WCPN) are in silence, switch your test radios between the two frequencies without changing anything else. That last part is important.
Do you hear the tone on every radio, every time? Is it on both stations, just yours, or none? Make it as fair a test as you can.
While you have all this stuff piled out amongst the Wendy's burgers, run one other test: while WBWC is in silence, switch the radios from stereo to mono. Does the tone fully go away, or just slightly or not at all?
Write it all up as simply, clearly and as non-confrontationally as possible, hand it to your engineer, thank him, then walk away from it. You've done all you can do.