Chez is very mature and probably the fastest Scheme available. It's so good that the Racket team is currently converting Racket to Chez as the backend language and compiler.
PS. consider it to be a Scheme really optimised for doing work with Qt. It appears that binding Qt well into another language is difficult (Python being about the only one where that was done successfully?), so I'm taking the approach of working "close to the metal" (C++), do things that are better done in C++ (like subclassing widgets) there, then making interfaces to scm as I go (i.e. make it so easy to make interfaces that this is a reasonable approach to do). That way I don't have to do all the work of binding the entirety of Qt, I can use qtcreator as I see fit, I can decide on a usage basis how to interface to a widget (modal in the Scheme view but not modal in Qt's view?, when does it need destruction in that case?). I guess the knowledge or abstractions coming out from this might be portable to other implementations, though.
Also again, I also do have code in another implementation (Gambit) that will have to stay there for the time being; communicating with the GUI via sexprs will of course be an indirection, but given that web programming could work the same way (the Scheme implementation on the server communicating with the one in the browser) it looks like the right approach to try for me. That will also mean that the approach will work with any Scheme implementation as the server (Chez, Chicken, whatever).
The interpreter currently relies on refcounting for simplicity and to provide deterministic latency behaviour. It's (currently) a simple s-expression interpreter partially because (at least at first) I want to use it to interoperate with another Scheme system via sending s-expressions forth and back, and then that's the lowest latency option. I've got various ideas in the areas of debugging and typing that I'll try to implement, and if I succeed on that path and start wanting to use it as the main Scheme system then I'll certainly move on to compiling to byte code or use a JIT.
I just started a month ago, and have to nail down licensing with my employer, when that's settled I'll publish the code.