Is there a way to uninstall a module/routes so that I can create something like a servlet container? In other words, I'd watch for jar changes and reload an 'app' without shutting down the ktor process?

So you want to make a some new routes/modules version available without shutting down the entire server right? It seems you are talking about multiple instances + load balancer + registrator solution. Have a look here, this may help: https://www.nginx.com/blog/service-discovery-in-a-microservices-architecture/

I have a very simple server at the moment. I'd rather not pay for extra Linux servers and a load balancer just to smoothly update code. I also would prefer to handle redeployment logic within JVM code, rather than by killing and starting unix processes.

Does your server support docker containers? you dont need to pay extra servers if you have access to containers. If you go that way, you can also do really nice things like A-B testing to see if your new instance/version is working fine after deployment.