What's your best advice for planning for late in June? Our first day in parks will be June 26th, our last day July 2nd.
My advice would be to plan to do rope drops when possible and avoid MK on Saturday. Since you're leading up to the 4th of July, I think the crowds in general will increase every day so I would do as much as possible at the beginning of the trip. If my family was going for those dates, this is probably what our schedule would look like. For the record, our kids are ages 16, 14, & 10 so they can tolerate long days; we do very few (if any) table service meals; and our kids can take or leave the character meet & greet's -- they'll do them if there's little or no line but don't want to spend time waiting for a picture with a character when they could be riding rides.

Fireworks and parades are not "must do's" for us. If they fit in our schedule, we do them; if not, no big deal. We like to try to alternate "long" touring days with "short" touring days so we're not completely exhausted by day 3. We also like to "front load" our week by doing a full day in each park during the first 4 or 5 days so that the last few can just be spent going back to things we missed the first time around. It also allows us some flexibility to rearrange things if we have a very rainy day during the beginning of our trip.
6/26 - MK - Rope drop until closing or however late we feel like staying (most likely with a break in the afternoon). We would probably not do MSEP or Wishes that night but take advantage of shorter lines during those things and ride the rides.
6/27 - AK - This is usually a short day for us so it would work well after a long day at MK on Friday. We would probably schedule our first FP+ for 10:00 - 11:00 so we could sleep in if we wanted to. Evening would be spent doing a TS dinner, special event (like a fireworks cruise) or just hanging out at the resort/swimming.
6/28 - DHS - Definitely a rope drop day for us so we can head straight to TSMM and ride standby and then ride it later with FP+. We would probably be finished at this park by late afternoon so we'd head somewhere for dinner (most likely in Epcot) and then back to the resort.
6/29 - EP - This would again be a rope drop day so we could ride either Soarin or TT in the standby line (we would get FP+ for the other one). We would probably spend the entire day at EP and possibly stay for Illuminations. If we're too hot, we might head back to the resort in the afternoon and then come back to EP to finish up World Showcase another day.
6/30 - This would be a sleep in day. Then we'd head back to one or two parks to catch things we missed earlier or want to do again. This is a night we would possibly head back to MK at night just for Wishes and the later MSEP since we would have slept in this morning and not be too tired.
7/1 - Sleep-in day or maybe a special breakfast. Then we'd head to Downtown Disney and head to a park or two for a few hours. We would go DHS for Fantasmic if anyone was interested.
7/2 - More re-visiting of a park or two and time at the resort to swim and pack.
Like I said, this is how
our family would do things -- your mileage may vary.