At last, some progress! I took the time to write up a full bug reproduction with minimal code at http://www.scirra.com/labs/chromebug/. That should really help Google engineers figure out what's going wrong, since picking through the entire runtime would be really tough for them.
While making the bug repro from scratch, I actually found a workaround - it seems the way you handle mouse events affects the delay in keyboard input! Anyway, I made a tweak to the Mouse object to include this workaround. You can try it here:
Just paste the runtime.js over your <install path>\exporters\html5\plugins\mouse\runtime.js. For me, this fixes the keyboard-input-delay bug. However, since the stuck-keys bug is so sporadic and rare, it's hard for me to tell if it's fixed that too. So could you lot try out the patch and see if you can get the stuck keys bug to come back? If everyone tries for a while and nobody can bring it back, it may also be fixed... but it will be hard to tell unless loads of people test it and we can be sure it's gone.
I think even without the workaround it's a legit bug in Chrome, so it's still useful to have it reported and hopefully fixed regardless.