Since most of the respondents on here say you should stay away from WS I am going to assume they have not been there. I go every night except Fri and Sat when I am there
1. On most nights during FW Epcot is fine. It is more crowded than normal. I think it's a combo of the festivities and the fact that the booths just take up a lot of space. You are really less likely to get rammed by a stroller than after MK fireworks IMHO. (I have never heard someone say that they were using their stroller to clear a path at Epcot. I did hear A woman shout "follow me I can clear a path" as she literally shoved that stroller into people at MK) . The fans there for the bands are generally either in a concert or on line

. (And some people do start lining up at 11 am)
2. But you have hit the bigger problem. The most popular park to evacuate to is Epcot when the MK closes early Probably because it's the easiest to get to on the monorail. Those families will be on the rides. Do not assume everyone is at the festival. The entire park gets crowded with the people coming from MK and the other parks.
And my only injury at a park was at Epcot in the middle of summer when some brat on those skate shoes lost control and hit me. I'll take my chances with the strollers.