Wish there was an even dumber alternative to Beanstalk. I've been tempted to build my own thing to get closer to my ideal of uploading a jar and forgetting about it.
(Raw javascript / vertx / postgres for actual development, but these aren't SaaS)
Current project uses GCP App Engine "Flexible" which is easier and seems to be built on better foundations than Beanstalk. Build a docker image and run. Although like you we could skip the docker shenanigans and just need a JRE to run our uber .jar (distroless https://github.com/GoogleContainerTools/distroless/tree/mast... makes a basic JVM docker container easy)
I self host it on a $5 droplet.
It does a good enough job of staying running once it's up though, so at least it's easy to forget why it was a pain to set up.