Here's a random idea I thought of yesterday because of all the recent talk about the Dungeon Finder and the deja vu experience.
My theory is that there exists certain players who are more successful than other players when it comes to random groups. Maybe it's skill, maybe it's gear, maybe it's patience, maybe it's even luck. But these people are more likely to successfully complete random dungeons than the "normal" player.
What if we could identify who these High-Success players are? It would be as simple as looking at their success rate for heroics where they queued solo, and comparing it to the average success rate.
Once you've identified who these players are, then when a heroic group is in trouble and needs a replacement player, instead of taking the first person in the queue, search the queue for High-Success player and toss them into the group. If the heroic group has wiped, and people have left, adding a stronger-than-average replacement would make it more likely that the run would still succeed.
You would make it more likely that runs don't completely dissolve. You refrain from throwing the first player in the queue, who might not be able to handle a weakened group, into a half-finished run that may not be successful, leading to a wasted queue and poor experience.
Plus, this would be entirely invisible to the player base. You can't really tell that something like this is happening. The High-Success player gets a bit shorter queue, but at the price of having to "carry" a weaker group.