The more examples we can get of this the better.
EDIT: Ok, I see Javascript is your thing ;), do you think doing it in JS has strong advantages over Clojure(Script)?
If you are not entrenched in the JS world, I would look into Clojure(Script). They've got a lot of really cool stuff going on.
I have significant mental investment in JS, and I work on the JS debugger for Firefox, so I feel like I need to be a heavy user of JS. Also I know so much about all the little corners of server/client JS, package management, how to deploy, etc. I don't think the return would be great enough to re-learn all of Clojure's tools.
If I were to start on certain types of apps (high-performant data modeling, or anything that requires special care about complex flows), I may look into Clojure. But honestly I'm interested in starting to write games so I'm probably going to spend mental energy learning Rust.
You're correct about it being sort of awkward at first when you are figuring out how to structure an isomorphic applications. It gets even weirder when you only use JavaScript as a compilation target.
I created an example isomorphic Clojure and ClojureScript application (https://github.com/domkm/omelette) and wrote about how it works (http://domkm.com/posts/2014-06-15-isomorphic-clojure-1/). It was an interesting experience. I wouldn't recommend it for production quite yet but I'm looking forward (and working toward) the day when we can easily deploy isomorphic applications that are not written in JavaScript.