Examples include Bastion rules, ship to ship warfare, strategic warfare, etc.

More generally, I'd love to hear what game design should tell me about mixing two different games together in order to tell a single story.

I want a simple story about war and conquest to influence the far more important story of the PCs. The MCDM rules or the Unearthed Arcana rules could work, but they're about battles rather than wars, so it'd take a bit of work to extract the story I want it to tell.

There's a LOT of options out there. I really want something simple. If you don't have better advice, I'll go with Diplomacy. (Or a Diplomacy variant? I don't know the game well, and it should be about war not diplomacy.)

Have you ever done a review of some of the systems that people have put together for strategic wargaming while telling a heroic story alongside it? I want it at the level of a war. A turn should be somewhere between a day and a month.