Anyone else feel this way, with AW specifically?
With Apocalypse World, I very specifically
never feel this way. It's the only reason that I've been able to run 10+ sessions with a smile on my face. I've absolutely felt this agony in other games, D&D is a big culprit, but even Burning Wheel and Dresden Files tends to give me this sense of "Man, that prep is a lot of work" sort of feeling.
This is because my prep with Apocalypse World is the occasional letter from the MC, and every couple of sessions or so I clean up my relationship map, or reprint my threats and fronts.
Maybe you could explain what you are doing in that hour of prep?
And maybe you should talk about how your actual game sessions go. What makes you think that you are responsible for bringing the fun? Nothing in the MC section says that. There is some expectations to make sure the player character's lives are not boring, but the MC moves and the threat moves allow you to challenge that on the fly.
Fun in this game seems to be designed to act as a group effort. The MC does his moves, and the player characters respond. The Characters act, and the MC responds. There's a push-pull that must happen for the game to achieve fun, and part of that process involves player involvement, and is out of the MC's hands.
Again, I have no idea how your game sessions are going, but maybe you might want to talk about what you think the responsibilities of the players is supposed to be. And compare that to what they're actually doing at the table.
That might get to the heart of this odd pressure to perform. I say it's odd because I've never felt that way when playing Apocalypse World, and it's one of the only games for me where this pressure is not present.