At work, we are nearing completion of our new management UI version 2.0, which is a single-page Hoplon app that supersedes our C# MVC app.
The C# MVC app is backed by a large and complex MSSQL database. In the past we've dreamed about a from-scratch rewrite of the whole thing, starting with using Datomic or Postgres, but it was just too much work. Too many of our other systems rely on MSSQL/C# quirks and they would all have to also be upgraded.
So, in order to release a faster/better 2.0 UI, we decided to back the new SPA with the existing C# code. 2.0 has its own backend, and this backend gets data and performs actions using a combination of interacting with 1.0 over HTTP (1.0 also serves a JSON-speaking API) and by talking directly to MSSQL.
Once we have discontinued the C# UI, all UI changes will happen in Hoplon which is more flexible and resilient. Then we can continue to modify 2.0 so that it talks to C# less and less. Once it depends only on MSSQL, we can discard C# and are free to consider changing databases for real.
I can imagine other smaller-scale integrations would be possible by using Boot to emit pages that Rails serves. Whether or not you want to do this I think depends on whether you are trying to replace Rails or just augment it.
I'm sorry to hear you're frustrated by the cricket noise. I really do encourage you to pop into slack, if only to direct attention to posts here. I believe there is a Discourse plugin which sends notifications to Slack, and I will look into it.