What trans did your car have before? If it was a 4L60E IIRC you need a longer driveshaft when swapping to a TH350 if you don't have the correct length driveshaft you should start there...
Is the TH350 a freshly built trans or is it used? If its used it could have internal damage. Generally a bad trans mount in these cars only results in a bang when your driving and hop on the loud pedal.
-1994 Trans Am Gt: caged, CC503, Garrett GT45, 6Lbs, 3.73
-2011 Camaro SS convertible: Sold, bought it back still stock.