Bad vibes

Just got my 360 in my dart. Runs strong and doesn't miss. Has the correct balancer and b&m flex plate. Doesn't vibrate in neutral when I rev the engine. Going down the road about the first couple miles when I floor it, it vibrates like hell feels like the trans is going come through the floor. Drive a ways further and floor it not as bad. Go maybe 6 or 7 miles floor it and vibration is totally gone. Let the car cool down and same thing all over. Has new motor and trans mounts and nothing is hitting anywhere. Never did this with the 340 it just had in it. Please give me your opinions. Thanks.