That's about as far as you can go with Java, I guess, but honestly, now that I type that out, I guess that does get you pretty far...
The most salient problem is the fact that the languages do not distinguish between references and values (aka “mutability by default”) which means that the compiler will not maintain those invariants for you unless you annotate things specifically, and the authors of the libraries you use do the same.
My overall preference is for F#, which is ironically a better object oriented language than C#, by virtue of using ML-like syntax instead of C-like. Nonetheless, C# is a passable functional programming language these days, and the language designers keep adding more functional-inspired features with every release.