Personally I would leave the boat at home. I know, hard to think of but a lot of lakes well have boat rentals and for the problems that you might encounter along the way might not be worth it. It might get you more time on the water with a boat rental and bring it back to the docks and let them take care of it. If you have to have it steamed cleaned after each lake you drop it into that is going to take a lot of time. I know while I lived in MT they had inspections all the time for Flathead Lake and I don't care if you only moved the boat from Whitefish Lake to Flathead Lake (about 20 miles apart) you were supposed to have it cleaned before using it in the other lake. I used mine in Flathead Lake all of the time so I didn't have to jump through any hoops t use it. When they asked what waters I had been in I told them only Flathead and they were ok with that.
Also you have to take into consideration how much it is going to cut your fuel mileage puling a boat for thousands of miles and the wear and tear on the trailer on some of the roads, also the damage that could be caused to the bottom of the boat from all the road construction along the way, which there well be plenty of. You have a very expensive boat and I'm sure you would like to keep it in good shape.
When we went in 2013 there was road construction everywhere and miles of it at one time. Then you always have someone that is going like a bat of He!! going the other way throwing gravel everywhere. I always pulled over as far as I could and lots of time it is n a soft shoulder which wants to pull you into the ditch.
Just a suggestion and I know you would like to have your boat with you, you'll have to decide if it is worth the effort and possible damage to the boat.