Full disclosure, I work at Fly.io now.
This exact setup is easier on Fly.io - our proxy layer runs in 20 regions worldwide with anycast, so your requests hit the nearest region and quickly terminate TLS there.
You can also run any Docker container, and either choose regions to run them in, or just set the min/max and ask us to start and stop containers in whichever region has demand, so your deployment follows the sun.
I really like Fly and would love to move some side project workloads to it, the only thing holding me back is the Postgres product which seems to be a little bit 'not ready for production'. I'm referring to point-in-time recovery and ease of backup restoration mostly.
The product looks too good to be true, and when you dig into a little deeper it seems like it isn't totally 100%.
Amazon RDS is something that I really trust, but I didn't get the same vibe looking at Fly Postgres.
Ultimately, we think devs are better off if managed database services come from companies who specialize in those DBs. First party managed DBs trend towards mediocre, all the interesting Postgres features come from Heroku/Crunchy/Timescale/Supabase.
So we're "saving" managed Postgres for one of those folks. For the most part, they're more interested in giving AWS money because very large potential customers do. At some point, though, we'll be big enough to be attractive to DB companies.