There is a TSB that covers this very thing. I have a 2001 and am experiencing the identical symptoms. The TSB can be found for free online here
http://www.fcsdchemicalsandlubricant...tsb/031515.pdf
for the 2001 in consists of slotting some holes and going thru a specific procedure to "neutralize" the engine in its mounts. The flate-rate labor for this TSB is around 3.5 hours. Different years have different procedures. I'll wait til warm weather and probably do it myself. We've lived with it this long, we can wait til spring.