Is this a valuable guitar? Still under warranty? Is there anything special about it, or is it a workhorse instrument?
I'd try the simple thing first, and experiment in a way that is nondestructive. Then, if you locate the hot spot and can learn a little about how it responds, you will begin to see options. You've done a little of that already.
How does the guitar change if you roll up a t-shirt and stuff it into the soundhole? (I'm not kidding) Does the sound get dampened all across the board, or just a little in the bass end? Does it sound
better?
Do you get the same unwanted resonance playing it tighter to your body than you are used to doing? In other words, does it change in any relevant way if you dampen the back only?
What happens if you tape a washcloth or small towel to the inside back of the guitar? (Use masking tape!!) Underneath portions of the top? Which frequencies change?
I'll echo Major Tom a little here. If you do your own work, you'll be familiar with the internal bracing. Look in there with a mirror and poke around to see if any braces are loose or broken. Something may not be doing its job.
The low resonant frequencies of the guitar will become enhanced with a thin or lightly braced top, and the trebles are enhanced (within reason) with a thicker or more stiffly (heavier) braced top. So if a brace is loose but isn't buzzing, it is not stabilizing the top as it should and you can get wolf tones popping up in odd places. Check to see the condition of the back plate (the extra reinforcement piece directly underneath the bridge, nestled in the lower central part of the X- brace).
You can experiment with adding a little mass to the top by using a small office supply clip on one of the top braces. Do this a little at a time; there will be a spot - somewhere - at which there may be a radical change in sound. Try to locate it with some precision and your options will open up. For instance, a cleat glued directly under a hot spot will enhance the mass of the top at that point and will change the sound.
Once you've gone through all the nondestructive ideas you have, you'll have developed a list of options. Then consider whether to take it to a tech; it is the easiest thing in the world to make a real mess with glue and a razor knife...
If you're really into this, you can experiment with clean glitter (or clean sand) and sound. Placing a speaker inside the guitar, you can send it a tone of a given frequency and measure the top's response graphically by sprinkling glitter on the top. As it resonates, the glitter will form a pattern that is a signature of that frequency and the particular build of the top (as affected by its attachment to the rest of the instrument). There are keys for different body types that contain signature information which may become useful to you.
Do a Google search for the Guild of American Luthiers (back issues of American Lutherie) and you will find technical discussions of this concept. Another source is the online Musical Instrument Makers Forum (
www.mimf.com ) which has highly moderated threaded discussions and a body of archives that will astound you. Another name to search for in this area is Rick Turner, a luthier who is active in the diagnostics and new ideas area of the craft. (The co-founder of Alembic and currently builder of the Renaissance guitar lines).
Finally, do a search of the term
Helmholtz frequencies and it'll open up an acoustic can o'worms. Have fun!