It will probably be tough, but as soon as you know start checking. A lot of people finalize plans the week before they leave and cancel their unwanted. I don't know about multiple groups being able to get the same ones, but you can try to get similar times, and then check in together(early for some) and ask if you can be seated close to each other, and they may be able to accomodate if you are willing to wait. If you are already down there and still looking, people have to cancel by 10pm the night before to avoid getting charged, so it's a good time to check. There is also a cancellation thread on here for your month that you can keep checking, and try to coordinate if someone is cancelling what you want. As PPs mentioned, may be able to get some of the less popular and at off times, like 8:00pm dinner. Epcot has the most restaurants, so the most choices. I have seen Coral Reef (where you eat by the aquarium) open close to my dates in the past.
I agree with PP though, that you could make some now, and can always cancel once you know your schedule, but some may work out and you would have those. If you have to cancel you can post here on the cancellation thread, and make others happy who are trying to get something. Quick service may also be your friend, especially for a group. Sunshine Seasons for example in Epcot, has a large seating area and a variety of stations with choices from chicken to Chinese. Flame Tree BBQ in AK has ribs, and Columbia Harbor House in MK has clam chowder and lobster roll. So it is not just burgers and fries! BTW, I would avoid MK on the 4th(they do have same fireworks on the 3rd, which is slightly less crowded, but still very mobbed) and you could check Josh's easywdw site for his July calendar, and his recommended parks for those days, to plan where you might want to be those days to coordinate where you might want to eat and make FP.
*Myers2170 - just realized you were the same person I was posting with on the "first time on property thread" with earlier, and so you probably know a lot of these places, since you have done WDW several times - sorry for repeat info.!