What's the problem with digital controls? My Sidewinder Pad has served me well through many a 3d game. The only game I thought would benefit from analog controls is Kurukuru Kururin.
If you absolutely, 100% need analog controls, use the touchscreen for that. You can use it with your thumb. You can't use both the touchscreen and the dpad (or ts + buttons), but you can't use the analog and digital at the same time on the PSP, either. With the DS you can at least choose whether you take the dpad or the buttons, with the PSP you always have to swap the dpad for the analog stick.
BTW, that analog looks like it's in an awful, cramp-inducing position.