I've put together a sort of idea for what to do with Grant Gardens, I doubt any development will ever be allowed on it and with Everton park so close it virtually unused. How about letting it Naturalise.
I expect the city council look on a huge open dpace that gets cut with a ride-on mower once a fortnight in summer as the cheapest option, but I can say from experience (my old house overlooked the Gardens) that it can be a bleak auld space. The simple arrangement of paths (one long one bisecting it from front to back gates, and a semicircular one to the side gate) should facilitate a straightforward division into zones like you suggest. A few more trees to break up the open space really would help too.