I run a 'well tweaked' 126 engine in the back of my 500, sitting on a standard 500 rear mount. Although it has a 'hotter' cam (35/75/75/35), I have retained the standard push-rods and cam-followers (new, as one always should do with a new cam) and have not suffered vibration problems---to the point that when I had my Dellorto FZD set up on the local 'Dyno', the operator pointed out how smooth he thought the engine was, even at 5,200rpm. So, the answer to your query is this---the retention of standard cam-followers and push-rods should NOT be a contributory factor with regard to your engine vibration.
Reading all the various comments,it would seem that a possible cause is that the engine is not sitting 'free'---have you checked the 2 gear-box mounts? If they are broken, the gearbox will sit on the cross-member, and therefore transmit vibration through the car.