Dear Ms. Shape
     Although you do not mention Food Grade Mineral Oil in your choice of
non-chemical acaricides, I would like to suggest that you visit the following
web page.
www.beesource.com
In this site you may be able to read about research with Food Grade Mineal Oil
findings for the last 5 years.
      And yes, Food Grade Mineral Oil applied with a Burgess Propane Bug Killer
(that is the real name of the machine) has been demonstrated to be effective
against tracheal mites because the fog produced penetrates the trachea where the
mites are located killing them.  And by the way, it does not harm the bees when
the mites die.
I will be glad to answer your questions, should you still have some after
reading the material on that site.  You may contact me at:
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Best regards.
Dr. Rodriguez