TL;DR: Jane Street is a quantitative trading firm whose language of choice is OCaml and has several people programming in it full-time. Besides experiencing the commonly-cited advantages of FP (productivity, expressiveness, local reasoning), they also found it highly performant, useful for rapid prototyping and resilient to changing requirements.
By "several people programming in it full-time" you mean "everyone who writes code in the company (IT, developers, researchers and traders) writes code in OCaml" right?. Yaron has said (perhaps in that video, perhaps somewhere else) that the founding partners (who were voice traders, not programmers) learned OCaml as their second programming language, after VBA. The language pervades the company.
I haven't, but the large company I work for has a product partially written in OCaml. I came across it in source control once. I'd guess it's tens of thousands of lines of code, but that's a complete guess.
Edit: By 'production work' I meant built things that are being used by other people.