I had a similar problem and the only remedy within reason was MOVING. The remodeling needed for a cure was beyond question because of the cost.
If you have the time take a look at this site re noise and its psychological effects on people. (www.anstendig.org) I'd like a pro's opinion. Read what they have to say about the effect of vibration and mechanical sound on us. What do you think Doc?
Also, the term "white noise" I believe, refers to something like white light, in that the energy is distributed uniformly throughout the spectrum/frequency range. White noise exhibits a flat distribution of energy with frequency. Pink noise, on the other hand, has higher energy in the lower region. Typically it means a 3db reduction per octave as you go up.. Anyway I doubt you have "White noise" coming out of those godforsaken ducts. Just plain old garden-variety crappy noise and it's going out of those ducts straight into you and your patients!
Hope you solve your problem Doc. Pehaps unorganized sound (noise) can be as unsettling and destructive as organized sound (music) can be soothing and meaningful. I do, in a general way, agree that there is geat power in what is heard. Music, sermons, hypnosis... (read those articles). I would like to hear your opinion.