Large tour groups have nothing to do with FastPasses running out. The same number of tickets have to go into a FastPass machine one at a time. It doesn't matter if a dad is feeding in 4 for his family or a tour guide is feeding 400 for her tour group. The machine spits out one FastPass at a time for one ticket at a time.
If there were only one FastPass machine at each ride tour groups would have an impact, but there are at least 6 at every ride I can think of and the Cast Members are there to make sure each of the machines are moving along. If you get behind a tour guide person and you really feel that you are running the risk of not being able to get a FastPass, ask a Cast Member to place you in another line.
Along with the tour groups, there are twenty thousand other people in the parks with you who want to ride Rock n' Roller Coaster and Toy Story Mania, too. It's just the luck of the day - how busy the park is, how quickly people take advantage of the FastPass system, and how late the park is open.
Believe me, on a day like the one you are describing, when FastPsses are out or return times are late in the day, that would happen whether or not any large groups were in the parks.
If you are there early - and that does NOT mean you get there around 10am, it means at rope drop - and you go directly to the ride, you will get a FastPass for at least a time before lunch. As soon as that time window opens up, go get another set of FastPasses. Even on a busy day you can get FastPasses for two or three of the busiest rides. And yes, you must be willing to stay and take advantage of the return time. It's not Disney's fault if you get tired and don't want to come back.