Power Tile Combo: Initiative combined with Crusade
As you said in the question, Crusade gives you ☥ for units killed in Battle.

As you also stated correctly, the effects of the Initiative happen before the Battle. (The power tile itself shows that it's a day phrase tile, not a battle phrase tile.) Therefore the kills of the Initiative won't generate ☥.

And there is no mystery with the Escape DI card: it cancels the Battle. Therefore effects before the battle phrase can't happen. Therefore the Initiative tile won't have effects.