I hate to say it but mine is smooth. 2008 Suzuki 9.9 with kicker tilt, alternator, electric start, 25" shaft, etc. I have mine mounted on an OMC heavy bracket on a 2502 older Trophy. Maybe if it was on a lighter boat it might vibrate? Or lighter kicker bracket?
It has a little vibration through the boat when in high throttle, but no more than my 20 horse two stroke or 15 horse 4 stroke Merc I had did. I think you have a bad motor. Mine certainly is not unbearable. I am very pleased with mine. I bought a pair of 175s to go with the new kicker. I would be surprised to hear that Suzuki would not help you as they have an excellent reputation.
Call my buddy Doug, at Performance Marine, in Everett Washington. He is the one installing the motors for them.
Good Luck.
Ron