I connect to the world through a satellite link. This means the MINIMUM packet time is around 800 ms, and 1.6 to 2 seconds is far more likely.
So I'm looking for multiplayer games that don't require twitch responses. E.g. flight combat games where I'm shooting at where the enemy was two seconds ago, and where my bullet's parameters take another second to reach the server is just not going to happen. On the other hand strategic games where you set forces in motion to continue in background should work quite well.
What to the folks here recommend?

I recommend Heroes 3.

^ agree
Try some turn-based strategies. Heroes of Might and Magic, Civilization, Colonization...