Help Please! Spatial analysis for disaster events

I am trying to create a definition that will analyses the walking catchments of existing open space and suggest the location and form a new open space to eliminate areas that do not fall within walking distance catchments. This is from the lens of open space within a city been safe areas of refuge during disaster such as an earthquake or fire.

Open space can be viewed as having an area zoned as calamity buffer framing a safe core. This has been modelled by offsetting the open space shapes by -15m. However my definition does not capture the safe core of an open when it divides into two or more. How can this be resolved? Picture of this problem is shown below.

The parameters for my next steps are:

Introduce new open space so that there are no areas not within a 500m walking catchment.

Maximise the area of the safe core with in new open space.

New Parks are to be located in the area identified from buffing existing park cores 500m.

New parks will also have a 500m catchment from their cores.

Archive the elimination of land not within a 500m walking catchment with the introduction of the smallest amount of new open space.

New open space should not have dimensions less than 70m*100m (though this could be a variable to determine different configurations).

There should be only large park (relative / variable) within a given area (Variable figure – could start at 1000m).