See, I think this is a case where some interesting ideas are being shoehorned into a new mechanic, when I think they would work perfectly fine executed a different way.
An idea is only shoehorned if doesn't work elegantly, regardless of other possible executions. Entirely a possibility for a specific implementation (possibly including my off-the-cuff ideas), I'll grant, but I fail to see how this idea is, from first principles, a round-peg/square-hole situation. Whether something like ED should be adopted depends not on if current implementations work fine, but on if using ED would be, on average, even better.
Firstly, all this is about how you gain dice, not how you use dice - which doesn't get rogues away from Sneak Attacking. Secondly, your first option doesn't really do anything new - it's the current Sneak Attack rule but with dice added - and your third option would be an automatic gimme for most ranged builds.
As I mentioned repeatedly, there should be a wide variety of ways to use the dice. I concentrated on how one gains dice because the discussion seemed to tacitly assume that would be the same as for the fighter, while there had already been discussion about spending them in different ways.
I don't consider the first option mostly replicating the current feel of sneak attack to be a demerit. If ED is a good option, it should be able to do at least as much. (My modification to require starting one's turn with combat advantage to get ED, and therefore damage equivalent to sneak attack, is simply my preference to liven things up a bit.) The third option is not an automatic gimme for most builds unless not-being-hit is a gimme. If that is the case something has gone horribly wrong at a more fundamental level. In any case, these are just my attempts to show that ED could, in principle, be utilized to achieve feels far beyond what is just present in the playtest fighter. The suggested mechanics are not serious attempts at balanced design, so I feel like you may have missed the forest for the trees.
And in a sense my examples do get rogues away from sneak attacking, because ED are a resource that can, I hope, do more than replicate sneak attack, and indeed there could be implementations where a rogue has ED but can't sneak attack. (Example: A rogue using the third option has ED in a system where "sneak attack" is defined as rolling ED damage twice against targets attacked with advantage. If this rogue cannot obtain advantage from any of the targets they would not, in this implementation, be sneak attacking even if they applied the ED as damage on attack.) Thus we could move away from the assumption that sneak attack is the rogue's combat sine qua non. So ED could do something that looks like sneak attack, as well as other things, but we don't have to call it a sneak attack unless that fits the usage.
There are other ways that Sneak Attack can be modified that don't require dice. We can already see them built into themes - the Thief gets Sneak Attack by being better at stealth, the Thug by flanking.
If flexibility is what's required, why not let Rogues do else than damage with Sneak Attack? The Complete Scoundrel gave an option for sapping people unconscious as opposed to backstabbing - you could build similar options in now.
Hopefully the above made it clear that's part of my goal. It's interesting you mention Complete Scoundrel, because I took a look at the 10 ambush feats in that book. The benefit summary of every single one starts with "Trade nd6 sneak damage to..." Hmmm...if only there were some
dice-based resource one could spend for unique effects...

OK, that's more snark than you deserve. Still, the playtest specialties offer different scenarios (catering to different playstyles and flavor of rogue) in which they may gain sneak attack. The different ED refreshing ideas have similar intent.
As other people have noted, encounter-based powers (perhaps where Warlords have to choose at the beginning who they are going to empower and how much, but get to choose when to engage the effect) are more evocative of the tactical thinking of the Warlord.
I don't have a strong opinion about that, but one could implement ED as an encounter-based resource for the warlord if desired. Again, I didn't mean my mechanical suggestions to be normative, just examples of how one can achieve different feels despite using a common framework.
I'd also add that random mechanics are disengaging - the player becomes default passive instead of default active.
Some random mechanics are disengaging, just as some deterministic mechanics are disengaging, and this is clearly a YMMV situation. After all, rolling a d20 is a random mechanic. Shuffling a deck is a random mechanic. And even at the level of class powers, some people enjoy the challenge of not knowing beforehand what resources will be available. Fans of the Crusader class (from Tome of Battle) and every Wild Mage ever will think you're casting too broad a net here.
See, I don't think this fits the Barbarian at all. Traditionally, what made Berserkers different is that, unlike normal soldiers who get worked up in the midst of battle when adrenaline is pumping, they worked themselves up to a frenzy ahead of time so they hit the enemy going full-tilt when everyone else hadn't yet gotten into the swing of it.
A mechanism where you start with some sort of rage resource and then exhaust it round after round would be much more evocative - the Fighter is a methodical combatant who can go the distance, the Barbarian is a whirlwind of violence who can be outlasted and worn down.
Then make that version of the barbarian. I'm pretty sure ED could do it, which is why we shouldn't dismiss it out-of-hand. If something else can do it better, by all means we should do it that way instead.
Thanks for your thoughts.