I published a Glulx game with music (Beat Witch) last year, and I found that Gargoyle has support for sound, and I did most of my testing on that. Fabularium also has sound support.
Lectrote does not have Glulx sound support, though I hope it comes soon. (From the GitHub page: “Because this relies on the Quixe interpreter, sound is not supported.”)
Glulx games (which normally use Quixe), thus don’t have sound support if played online … unless the author does some fancy coding magic or uses a different interpreter, such as Vorple or Bisquixe.
I can’t comment on timekeeping support, other than the fact that I’d expect a good number of interpreters would, and any interpreter that allows you to work with JavaScript (like Vorple) would most likely have a way to work with that. You may want to create a small game to test different interpreters on.