This didn't turn into a gentrification issue as it is very much a class struggle issue from the beginning. (And as such, a gentrification issue.) Kids don't have money to pay to play, so they can't even share the field?
It looks like this was a similar situation, so why would anyone feel "slighted" because someone made a reservation?
Give up the game, but let people know about the reservation system; offer company funding to book community sessions; get someone else to do the enforcing so it's them who look bad.
So 96% of the time, the park is open to everyone and 4% of the time the park can be reserved for a price which is equal to 2.5 hours of work at the local minimum wage.
One could easily argue that the people showing an unreasonable entitlement are the ones who think they should get to use the park in the tiny sliver of time where someone else has paid the city to reserve it for an organized game.