I am currently weighing up the use of Elixir vs Clojure for running a web server to handle many concurrent Web socket connections. Now Elixir/Phoenix seems a natural fit for this and you see benchmarks demonstrating how far it scales (I doubt this has an bearing on real life load). But, most of our infrastructure is written in Clojure.
In our case, the websocket handler is almost completely independent from the rest of the existing code base.
So the question is - would you consider taking on another language/ecosystem because it is a better fit for a particular job? vs using a tool that is already a large part of your existing ecosystem.
And, does Elixir/Phoenix exceed Clojure/JVM by a significant margin under real world loads for this kind of task to justify using it?
You may find this conversation helpful.
In summary, the "speed of your webserver" is not going to be the bottleneck in your development. Coding, testing, debugging, refactoring, and other human-related tasks are more important by a ratio of 100x or 1000x for just about any modern project.
Since you are already comfortable with Clojure and using it for most of your project, I would strongly suggest sticking with it rather than split your codebase into 2 incompatible parts.