Unfortunately, I'm not aware of any web based solutions. I'm sure there are, but I haven't used any. You didn't mention a platform so this is for the Mac and iPhone and unfortunately, there's no web version either (sorry). If I may though, I highly recommend Things. They both sync up (mac + iPhone) which is really nice. But to meet one of your requirements: it really contextualizes tasks and allows grouping/sorting options on both Mac/iPhone so maybe this is something to (at the very least) checkout.
GTD is a bit generic so, I'm unsure if any (or the majority) of GTD apps specifically include meetings. Someone may know of an app of course, but I thought GTD was a very generic, template-able approach and meetings seem to be a bit specific.
But to address one point:
Note that to do list tools do not come
close to meeting my needs (at least no
to do list tool I have seen comes
I agree that most tools don't come close to most needs. Up until my trial with Things, I really felt that most to-do lists were lame, and at best pretty 'meh'. Things has really helped me organize and manage my time fairly effectively and if they had a web version with meetings, I think it would be perfect from what you described. I've been using it since January and at times, I wonder how in the hell did I lived without it. But I realize my recommendation doesn't meet all your requirements, and I thought it may be beneficial to at the very least look at a supposed 'to-do' list in another light.