Hi Dave,
My thoughts are you are having some sort of harmonic in your prop. Do you have another prop you can try? also, note the RPM of the engine when the harmonic starts, write it down, and then cut the rpm exactly in half at the same airspeed, (pull the power and dive), see if there is still a harmonic (it might be very small). Whatever you do DO NOT continue to run in the harmonic range unless you are over a large dry lake, or an airport!
-Tom