Thanks for all the comments and suggestions so far.

After another flight this weekend, I have some additional data on my
resonance issue.

During a very careful preflight, I noticed the elevator trim tab is a bit
sloppy.  The flaps are also a bit sloppy.  The ailerons aren't, the rudder
isn't and the elevator isn't.

In flight, I tried the following:

1. manipulating the elevator trim (overpowering it with the stick and
elevator); it made no difference.
2. climbing and descending; no difference, except when associated with
airspeed.
3. rolling right and left; no difference.
4. hard rudder inputs; left rudder seems to reduce the noise, right rudder
no difference.
5. flaps; hard to tell, I DEFINITELY get a resonance when lowering the flaps
1" at 140 KIAS.  But it is a difference tone (deeper).
6. gear; no difference, but by that time I am only doing 120 KIAS

Any more thoughts?

Matt