Don't miss the opportunity! I'm excited for you so I laid out an itinerary. Based on 2 days to get to Blue Water Bridge, you will need to be on the move for at least 12 days altogether. If you take 4 days for sight-seeing or weather windows, you will need 16 days. That doesn't count your preparation time, which could easily be 2 to 3 days, particularly since you say you are a bit inexperienced.
@duck21 had a remarkably similar trip with some differences that I will note. They travelled up the east side of Lake Michigan and the prevailing winds meant that he had a long fetch for wind-driven waves. Your safest bet by far is to travel up the west side of Lake Huron. If you stay close enough to shore, you probably will have a short fetch for waves with prevailing SW winds. I would leave as late in June as you can muster. As said, the water temp means cold air.
Here's your best bet for stops:
Blue Water Bridge to Port Sanilac 30 miles
then Harbor Beach 30 miles
then Port Austin 30 miles
then Harrisville 45 miles (first stretch across "open water")
then Presque Isle 50 miles
then Cheboygan 55 miles
then Mackinaw City 15 miles
then Beaver Island 40 miles
then Washington Harbor 75 miles
finally Sturgeon Bay 50 miles
If you can't take that time, then better off hauling overland. I agree .... don't bother trying for Mack Island marina. You'll love Mackinaw City. even more. Take the ferry to the Island, it'll be much easier and you won't miss anything. 50 to 75 mile days will be pretty long, so don't over estimate your daily mileage. Get into the swing of things early and easy does it.
Consider that your boat is small and lacking experience, don't push it. I think prevailing winds from SW will be a blessing on this trip! I'd love to make that trip but honestly, I'd need to do it in a more comfortable boat. I'm suspecting you are young and tough so the Hunter 27 will be fine. Assuming it is in good shape for a 2005 model with 18 Yanmar(?) you should have no problem making 50 miles in about 8 to 9 hours.
I think if you take the easy way out (overland) and don't take this epic travel adventure, you will regret it. Don't miss it!