If it were me, I'd make a clone of the track and invert the polarity of one. That gets you silence. Now, solo one of the tracks and try to get it to only have the noise you want removed using EQ and dynamics processing. Now, listen to both together. The noise should cancel from the original.
You can repeat this technique to make a reverse noise gate on the noise only track. A reverse noise gate will give you only the soft moments and remove all the dialog.