Don't think there's a joystick specifically like you mean, the only two external controllers I know of is a paddle controller for Arkanoid and Space Invaders Extreme, and the Guitar Grip controller for Guitar Hero. Personally, I found the d-pad on the Lite to be a little uncomfortable as well, and switched back to my old fat DS. I thought maybe the Nerf Armor would make the Lite a bit more comfortable to hold, but I realized I really just liked the old model better, and got my money back.
Dunno about a case that's official and would fit with the Nerf Armor, might fit into an old case if you can find one used or something...I usually just stick mine in my pocket/backpack, and I have a seperate case for all my games.
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I'll brave the storm to come, for it surely looks like rain...