Advice on making custom non-real geographical maps

I'm looking to visually graph data about various parks in our system, ideally using a sort of pseudo-map for each park. BUT, I don't want real geographic maps - I want to compare parks to each other based on their generic features, ideally in ways similar to election maps or heat maps.

For example, I'd like the general shapes to be like this: image , but to overlay a heat map of where visitors are (or crime, or irrigation, or maintenance costs, etc.).

I've put some mock data here: Gist.

I know how to do geographic maps, but I don't really care to see these laid out geographically.

Is there a graph type that would do something like this? I thought a treemap might do it, but I haven't quite been able to make them do what I want - I want the areas to be fairly fixed (for now - maybe someday I want to change them up by area) and just the data on them to change. Or, do I need to make my own shapefile and if so, how would I do that?

I'm mostly a tidyverse/ggplot2 sort of person, so hopefully within that workflow if possible.