I have zero experience with bikes on boats, but have crossed to Mackinaw Island a few times and have some thoughts on the crossing.
First, you are very correct in wanting everything well lashed-down for the crossing. The Straits of Mackinaw are notoriously rough with exceptional and sometimes unpredictable chop due to the interactions of Lake Michigan and Lake Huron waters. Differing wind patterns, wave patterns, and air masses coming together can make crossings challenging - and sometimes very dangerous - in small, open bow boats.
Keep your schedule flexible so you can choose to cross when conditions are best. Back in the early 80s, when I was a teenager, my family crossed from the Cheboygan River to Mackinaw Island in sunny, glassy conditions at about 8:00 am. It was an absolutely perfect crossing. We got a day slip in the main harbor, and did touristy stuff all day. Just as we were readying to depart, about 5:00 pm, late afternoon atmospheric heating combined with the Straits geography to build an unpredicted and very harrowing chop. I believe it was 3-5' conditions, but the way they can sometimes stack, I am sure some we encountered were 6'+. We were in a late 70s, 19 ft Four Winns tri-hull deckboat with lowish freeboard. It was scary as hell. We made it back to the mouth of the Cheboygan soaking wet but in one piece. However, knowing what I now know... We were very foolish and very lucky that day.
You can cross safely and comfortably in your 19 ft Yamaha, and have a great time on the island, but don't cross if the conditions are not good. And beware that the Straits conditions can change, and massively intensify, in just a few minutes.
Of course, if you have experience in small boats crossings at the Straits, you know what I mean... and please don't be offended by my post.
Having said that, I am jealous. You will have a great time on the island. It is truly one of a kind.