Heroku has a feature called Error Pages which allows you to upload a static page that Heroku will serve if your deployment is unhealthy.
You can do this in the vm but there are certain failure states that would prevent a service from serving the error page so I think this is a good fit for the fly proxy.
I’m thinking if you include a 500.html (for example) in your image, and then link that up via something like statics, fly could read that file from the image and serve it in case of an unhealthy service…