Have you ever played a Grand Melee game of Magic?

I have played quite a number of Grand Melee games. Some quite large.

Speaking of multiplayer, do you know whether the predator-prey relationship of Vampire: the Eternal Struggle works well in Magic? It seems reasonable in theory as a way to make the game less political, but no one seems to do it. (In V:tES you can normally only attack the player to your left.)

There’s a multiplayer format called Grand Melee that used to be popular. In it, you attack to the left. Your spells had a range of one (you could only affect yourself and the player on your right and left). The format still had a decent amount of politics in it.

Is there any multiplayer format designed around three players dueling each other?

Not that’s gotten a lot of attention. Grand Melee is my favorite way to play with three players. You sit in a circle and get a point each time you kill a player to your left plus a bonus point for being the last player standing. (There’s more rules when playing with more than three players.)

"I don’t like a lot of politics in my Magic (although I truly get while others really enjoy it) so Commander is never really going to be my format." Then you're playing with the wrong group. Our group has no politics. We just do a bunch of stupid things like dismembering goblin arsonists or flinging squirrels at each other.

It is impossible without strict guidelines (such as Emperor or Grand Melee) for any Magic game with three or more players to not have politics. Perhaps you have a group agreement ahead of time but then you’ve just shifted the politics to the pregame. Be aware that I understand that there’s a lot more to Commander than the politics but there’s enough politics that it’s not my cup of tea. Once again,. that doesn’t mean I don’t think it’s awesome the format exists and that I don’t work hard to design for it, it’s just not how I choose to play.