Good idea about the umbrella for the little ones. However, what do we do with that while it isn't in use? Put our crap in it and wheel it around? lol.Have you considered taking a small umbrella stroller to use with one of the 18 month old twins when your 6 yr old gets tired? When the 6 year old is active, the twins enjoy the baby jogger. When she is tired, one of the twins can be in a small stroller that is easily transported.
We were there in May with our 2 1/2 yr old and 4 week old and lugged a city select around with the second seat and a bassinet. With the two of us it was a bit awkward getting on the busses but we made it manageable. Essentially the hardest part of travelling to and through the parks is our expectations of the kids behaviour and forgetting about how the kids are experiencing the whole situation.
With that said, our experiences with the busses was excellent. The drivers are patient and the other riders were relatively easy going even at the end of the night. Our plan of attack was that one of us was responsible for the kids getting on the bus and sitting, the other took care of the gear. Stroller was folded in line as the bus pulled up and we were ready to go once it was boarding time.