Finally did a bit more work on this. Selecting things here now selects them in the main editor window, and vice versa. Aside from this it still does nothing - so pretty much, minus the hidden hotkey stuff, it does exactly what the old one did too, but is written in a way that makes it much easier to add stuff to.
I'll probably include it as it is now, with no further changes, in the next editor update, just so that we have a chance to make sure the new list really is working properly in an actual usage environment (I'm not the best to test this myself - of course I've done some testing, but in real-world situations I don't tend to use the level list much, so I'd like to hear reports from people who do). Then, once we know the basic functionality is stable, I can get around to weighing up the suggestions here and implementing some of them.