Are there any practicioners of traditional Native American healing?
Obviously, the efficacy of ritualistic medicine hasn't been validated
by science, but I've been suffering from low energy, malaise, etc
(most likely mono), that I'm willing to try a spiritual treatment.
 Where can I find such practitioners that aren't doing it just for
money for touristy "entertainment value?"

You might contact the Woodfish Institute to see whether they can offer
you a good referral. Contact info is at the bottom of this page:

http://www.woodfish.org

Some of these links might be useful:

http://www.livinglibraries.org/shaman.htm

I have explored this avenue myself, and I can recommend two people to
you - Denise Linn and Almine Barton. I haven't met Denise Linn, though
I have used her products, but I have met Almine Barton and have
received a personal treatment from her. I'm sure there are many more
trustworthy individuals out there, but these are two people I know of
in this field, who have had a positive influence in my life.
    
Denise Linn's website
http://www.deniselinn.com/Aboutdenise.htm
    
Another site about Denise Linn
http://www.symbiosis-music.com/d_linn.html
    
Almine Barton's website
http://www.spiritualjourneys.com/index.html
   
    
I wish you well.