We go in June because I’m a teacher. We do get out at the end of May so we head down to Disney the first full week of June. I have found the crowds to be very manageable. The heat and humidity can be brutal if there is no cloud cover but last year we had a lot of cloudy (and rainy) weather, which kept it from being uncomfortable.
We do prescribe to the rope drop-midday break-evening and nighttime touring philosophy. One year I went with my parents and we could not get my dad up for rope drop. I belong to a June FB group and I was able to see how much the other group members were able to complete in just the hour or so that we missed every morning. So now, we definitely do rope drop and we accomplish a lot more than if we did not. However, if that isn’t your touring style, do what works for you.
I really enjoy touring the parks at night, so we usually close down the parks, even though I have a 4 and 6 yr old. What makes it possible is that midday break away from the hottest and most crowded part of the day. We all get a break from the stimulation and we get some pool or nap time, or both. We usually have about 4 to 5 hour breaks. We do drive, so we have our own car and we stay at WL which allows for the boat from MK, so getting back and forth from the break is fairly efficient for us.