One thing I'm curious about is whether player-initiated exposition is a good idea.

Normally, the DM has to take the initiative to explore your character's backstory. For example, he might say "You recognize the leader of the bandits - he was with the man who killed your father."

What if instead, when the DM has a generic group of bandits attack, you remain in character and just confront the leader of the bandits. "You! You were with him! Where is the man that killed my father?"

On the one hand, this forces the DM to suddenly improvise when he already has a lot to do since he's running the entire adventure. The DM might not like that. On the other hand, it also takes some of the work off of the DM, since it's no longer his job to make sure that your characters's backstory is being revealed the way you want it to be and he gets a memorable NPC for free.

If the DM doesn't want to roleplay a dramatic dialog right there and then, he can say something like

The man was just a hired thug. All he knows is that the murderer and his elite guards left in the direction of [city the players were going to visit later anyway].

The man was killed during the fighting, but you find half of a strange icon, the holy symbol of a god you don't recognize, hanging from a golden chain around his neck.

This way the DM can decide what the clue means when he gets around to it. Even if the bandit is just dead and the DM gives you no clues, you can roleplay your frustration. In any case, now everyone in the party knows something you (as the player) want them to know, even if it's not something you'd tell them in character.