I used Zappa a little bit a few years ago, and that was alright but not my favorite way to deploy an app. Since then, I've pretty much exited the AWS ecosystem and use GCP almost exclusively (though occasionally I am forced to use AWS). I'm wondering if you've considered using Google App Engine which has a generous free tier and doesn't have any of the CDN issues Zappa has. It's my go-to for web apps.
Whats the AWS solution for serverless task queues which autoscale containers and have scheduled jobs? I'm looking at Google Cloud Run as a queue backend, which lets me define tasks as regular HTTP endpoints.