Keyframed notch filter?

Hello,

As you can see from this spectral pitch display, I have some audio with a background tone that rises in pitch from about 4KHz to about 6kHz over around 7 seconds. This rising tone appears in the background around 15 times in my Premiere Pro sequence. Is there way I can create some kind of keyframe-controlled, or LFO-controlled notch filter to filter out this very narrow (but rising) frequency? I have successfully used Audition’s selection tools to remove this line from the spectral display, and it sounds good, but it’ll be pretty time-consuming to do this for each time the sounds appears, so I’m hoping there might be a shortcut! Any thoughts, anyone?

Thanks!

~Paul