Magic 2010: Take a Third Option
Proposed Rule Changes Alt-5 and 8 (Replacing new rule 5):
Rule Alt-5: Combat damage does not use the stack. When combat damage is dealt, players may assign damage however they like and that damage is dealt including trample damage. There is no ordering of blockers.
Rule 8A: Instead of creatures with lethal damage being placed directly into the graveyard, whenever the stack is empty an effect is placed on the stack that says "All creatures that have been dealt lethal damage are put into their owners graveyards."
Rule 8B: All effects that can save creatures that would be dealt damage, including regeneration, damage prevention and protection, are errata-ed such that they can also remove damage that has already been dealt.
Technical Note: Deathtouch would likely go back to being a triggered ability, and you can choose how it deals with damage prevention however you like.

Note that this change creates a different intuition for new players. There is now a universal, intuitive rule that all creatures can be saved in a variety of ways after damage has been dealt. My instincts tell me that unlike the stack there is nothing unintuitive about this and it seems easy to explain (e.g. "You get a chance to save your men.") and you can understand it without the stack. New players get a game that's easy to understand while old players get to keep using good old stack tricks.

The one issue I can think of so far with this could make cards that damage your own men more powerful by refusing to let the stack empty and thus keeping them alive, which may enable new combinations. It is possible there is a card or two we would have to alter to prevent this if it got out of hand, but there are a number of possible fixes for that.

Note also that yes, this is similar to the pre-6E system, but its problems were in large part caused by only allowing certain types of spells and effects during a special 'damage prevention step' rather than simply giving players a chance to do whatever they want.

EDIT: A dealbreaker objection now that I've considered it is that now you can't kill anything with damage while a stack is in progress, such as in response to an enchantment or a giant growth. One fix to to say that the trigger is whenever a creature is dealt damage or its toughness is reduced, at which point a trigger is placed on the stack (empty or not) for all creatures that were effected and are now about to die (or each creature triggers seperately, which we want to avoid due to Magic Online).

Thus:
Alt-8A: Whenever a creature is dealt damage or its toughness is reduced, and this results in it taking lethal damage, put upon the stack an effect that says "If this creature has taken lethal damage then place it in its owners' graveyard. If multiple triggers occur simultaneously, combine them into one trigger." I like that last sentence for other places too! This now creates the problem that when trying to save a creature anything that damages it all will re-kill it. I'm guessing that is the price we pay...

Thus:
This is why it doesn't work. Alas. You have to get more and more convoluted to avoid doing ugly things and while you're doing that add a lot of extra stacks all the time, making the game more complex. The lesson here is that the stack works the way it does for a reason. It is simple, it is elegant, and it gives us the game we love. Combat damage uses the stack because otherwise double blocking is an ugly mess (see new rule) and because it allows us to do all sorts of cool things. We've decided that we dislike the cool things, because they are 'not intuitive' and that the ugly mess is an acceptable loss towards that end. The attempt to make these things intuitive was a noble idea, but just like the actual new rules it ends up making things more complex and ugly in the name of making them intuitive.

I enjoyed thinking about that quite a bit, and I think I learned a lot about the game and the way it works. Kudos to everyone who gave me all the great feedback, which is one reason I love the internet. There is no way to cheat this one. I still can't help but feel like there's a better way to handle double blocking, but so far I haven't been able to think of one.