We have a similar design and use a 6 HP Tohatsu just fine, we get 5.5 knots at 20% throttle. I also believe James Baldwin @ Atom Voyages used the same motor without any trouble on his Pearson Triton. He claims he gets 5.8 knots in dead calm with a 6 HP Tohatsu:
Atom Voyages - Triton #503 Refit Part 1
If you are getting a lot of vibration and little power, you might take the motor off and have it serviced, that motor should push your boat fine. Someone told me that you need 1hp per ton of displacement with an outboard, I don't know how that scales beyond 28 feet, but so far it's proven correct for our experience.
The mount does make a big difference, being able to lower and raise it is awesome. Our mount is a POS, we are either going to build a well (see above) or get a better stainless mount soon, Garlick makes nice ones that are spring loaded to help with the weight of the motor. I'm really tempted to build a well this fall though, having the motor in the locker would be really convenient. I just have to be brave enough to cut the holes and build it out. Being able to raise and lower is key, though, as it keeps the motor out of the water and protected.
One thing to note, you will get a lot of people in here telling you that you need to put an inboard in the boat. While I do not want to discount their advice completely, I found more people that had made significant passages advise me otherwise. We were in a similar situation where our inboard was removed and the PO sailed the boat without a motor, we installed the outboard with intent of putting a diesel in. When I called to get a quote to put a Betamarine 14 in, the quote came in around $15k including labor, which is over 3x what we paid for the boat. The labor alone came in at over $7k. I concluded it wasn't worth it and kept the outboard, a decision which has proven to be a relief. The storage space it opens up is really nice, you don't have the odor down below, and maintaining the motor is easier. Just make sure you've sealed everything down below the waterline if you decide to stay with the outboard.
It appears that I can't read. For some reason, I thought you were using a Tohatsu. I can't really comment on the Suzuki's ability to push the boat, you might try a different prop and see if that helps. I'd also look for a mount that travels at least 15in.
You might consider selling that motor and getting a Tohatsu Sail Pro, the extra 5 inches on the shaft may help a lot, it'll allow you to get the prop deeper and is proven to work on the Triton. It'll cost you in the short term, just depends if you want to make the investment or not. We paid $1500 for ours brand new, I looked at used ones for ~$1100.