I feel for you. One of my sisters vacations on MV every summer (she lives in NY) and it's a giant hassle for her. Everyone expects to see her but getting off the island and going anywhere is a big PITA. So then she invites people to stay with her for a night at a time and that's a pain too. In the many years she has done this I've gone down to see her exactly once - we made it a day trip (I live about an hour north of Hyannis, southwest of Boston) and it was a long, exhausting day for everyone.
What I would suggest would be to split your vacation - my sister sees people on the way to MV and on the way back and that seems to work out well. They drive here but you would be flying in and renting a car, right? You can decide to land in Boston or Providence and then visit with relatives for a day or two, then go and relax for a solid week on MV, then visit others on the tail end of your vacation. You can definitely rent hotels for a night or two here and there. We usually end up going down to the cape at some point in the summer with very little advanced planning and have no trouble finding a place to stay for up to three nights.
I know you're kidding about the Mayflower II but seriously, my MIL rented one of the Cape Cod Canal party boats for an afternoon last summer for my FIL's 70th birthday and it was fabulous. It wasn't that expensive, she had Roche Bros catering brought in and the party ran itself. If you want to have a big gathering but not be stuck at someone's house, it's actually not a bad idea.