An intrihuing plan... Maybe a few refinements, but I like the concept. If you break up the trip to Bullfrog, better to stay near Richfield than Hanksville--that's closer to the halfway point, but if I were you, I'd plough all the way to Bullfrog. Of course, jet lag might not let you, so go as far as you can. But Hanksville is not worth the overnight, and it's so close to Bullfrog (90 minutes) that I'd just push on.
Defiance House Lodge is your best bet (one of very few) at Bullfrog... Failing that, the Ticaboo Lodge would work. No frills at either place, but Defiance is better. If you got there on Sat, you could boat on Sunday and Monday as you plan.
Key logistical challenge: getting supplies and keeping them cold. There is no major market at Bullfrog ( as there is in Page), just the marina store with some basics, inot tons, but milk, some meats, drinks-- better than a convenience store, not as good as a supermarket. Hanksville isn't any help either. Honestly, on your route St. George or Cedar City might be your best bets for stocking up, but then you'd need to keep things cold.
You can always eat out at Bullfrog...nothing fancy, but there is The Anasazi Restaurant, which is nice enough, and obviates the need to bring major food supplies.
Make sure you check on the condion of the road leading from Bullfrog to the Burr Trail (Bullfrog-Notom Road) before committing to that. It's only dirt for a few miles, and usually easily passable, but a storm would change that. Fortunatley, major storms in early June are rare. Once through the Burr Trail to Highway 12, at Boulder, reward yourself with lunch at Hell's Backbone Grill. Excellent, and a beautiful setting.
Escalante is a good base for many things if you spend the night there. Hikes along the Escalante River, Calf Creek Falls, many other things...
From Escalante, Bryce is right on the way to Zion...maybe 3 hours total to Zion if you didn't stop. But you'll want to take your time.
I could add many other details, but there's a do-able plan in there... Not the usual concept, but that's why it might be very cool... I like it...