You’d want to explore using Fly Machine apps then.
Fly Machine apps can be deployed to all regions. Since Machine app instances are created on-demand in response to user requests (in a region closest to the user), they are more cost-effective. These instances typically cold-start in 300ms. It is upto the instance’s main process to exit itself once it has serviced the request. For example, I have setup one of our Machine apps to terminate after 5m of inactivity. This blog post has more hands-on details on Fly Machines: Building an In-Browser IDE the Hard Way · The Fly Blog
At the outset, the stuble behavioural differences between regular Fly apps and Fly Machine apps might confuse / frustrate you, but once that novelty wears off, things start making more sense.