We had an issue, NOT NEARLY as bad as yours, when we backed up to park property that joined a golf course.
We called the city parks and recreation and they came out and fixed the area. No cost to us.
I've seen some stories on the local news about people practically losing their yards due to erosion and the city was working on the problem. I'd call the city, most especially before you invest any money and they say "you can't do that because it is city property".
We currently back up to park property that is heavily wooded and we have this area cleared back a few feet so that the heavy brush is not next to our fence. The city got on my case for this UNTIL I showed them video and pictures of the bobcats that sit there often. It is a safety issue....
Good luck..