I hve a 1995 contour gl which did the same thing I switched out the motor mounts wich 3 were bad as in the rubber mounting came apart.... after I replaced the motor mounts it still vibrated but not as much...

modifactions are a 2000 deck lid with spoiler, wood grain dash with Pioneer 50x4 cd player, 5 spoked alloy rims full bra, K&N air filter, tinted head light covers, fog lights..... I am looking for more ideas too modify my car any ideas.... 5% tint on windows... more mods to follow... cold air intake and new exaust.