The sound "sounds" like it is coming from the rear of the plane, but I can't
really tell.  It also "sounds" about the same as when I drop an inch of
flaps at 140 KIAS to get slowed down to gear speed.

Matt,

 

After ignoring this for quite awhile (correcting other items higher on my list), I have a similar problem.  However, mine seem to be rpm related, but does not sound like direct engine vibration.  I have recently replaced the elevator hinge pins with .005 oversized stainless "piano wire" that makes the elevator looseness completely disappear.  I still get the vibration at 2480 rpm and some lower settings, never in climb, always in an energetic pull-up, and nonexistent at WOT, 2700 rpm. ?????  When I listen to the fuselage with a stethoscope, I do not pick up anything special?  Right now I am investigating any possible engine to cowling contact.  Then, nose gear door.  I had the prop balanced this summer, but????