Sounds like a setup problem to me--or someone was messing with the truss rod to adjust action, which is not the purpose of the truss rod. It adjusts neck relief (or bow). I've read most Martins (esp. the "D's") come from the factory with a rather high action, which bluegrass players seem to favor. Probably this guitar's buzzing or tinny tone could be eliminated with any number of approaches--but here's what Frank Ford over on Frets.com has to say about truss rods-and he knows a thing or 2 about guitar maintenance:
"The single most common misconception is that truss rods are for adjusting action or intonation. While adjusting the truss rod does affect the playing action, that's a side effect and not the purpose for the adjustment. As a general rule, once the nut and truss rod are set, all action adjustment is done at the bridge, by raising or lowering the saddle. Intonation is affected by action, too, so correcting the action may improve intonation, but again, that's a side effect."

Maybe a new saddle (maybe bone) and a new nut and proper asjustment at the bridge and nut will eliminate the tone problems. Also, if someone has messed with the trussrod a good guitar tech or luthier could get proper neck relief pretty easily. All sorts of people think the material of the nut, saddle and bridgepins--not to mention STRINGS-will have the biggest impact on the sound. Worth looking into as a D35 is usually a cannon of a guitar.