1999 Cadillac Seville shimmy at 60-70

While driving down the highway doing 60 my whole car shimmies, you can feel it through the whole passenger area and feel it in the steering wheel. The engine mounts have been replaced, there are new wheels and tires on it, the front end has been aligned. The brakes have all been replaced the cv joints seem to be ok. We have had mechanics go over it several times but they say they don"t know what the problem is. The shimmy at first seems to be intermittant during the beginning of the trip, but becomes consistant as the trip continues. Under 55 there is barely a shimmy and above 75 the shimmy seems to disappear. Any ideas?