Recommend awesome games on PSP?

Yes, if you're planning for a perfect social link, you'll find yourself reading walkthroughs all through your gameplay. Because there are some time it's better to go for a Social Link and some times it's the matter who's going to be maximized first.

I like how people just stomp game names that require Analog stick to play while the dude clearly stated that his analog stick is off limits hahah

Half Minute Hero [very entertaining]

Darkstalkers: The Chaos Tower [from what I remember you can only use the d-pad]

Castlevania: Dracula X Chronicles [three games in one, however only Symphony of The Night has RPG elements]

Oh yes! Half Minute Hero is VERY GOOD. It's definitely worth the buy (or download if you're PSP is hacked).

Cladun This is an RPG is also another good game.

The Legend of Heroes Sora no Kiseki (Trails in the Sky)
[spoil]and The Legend of Heroes series!

I third recommend half-minute hero
Yggdra Union
Fate unlimited codes

Gawd I finished Persona 3.
What an ending, I've never felt so sad because of a video game.
Tears were almost shed because . . .
*SPOILER WARNING*

YES! Definitely this! Hopefully it shouldn't be TOO analog heavy.

Also, my bro just told me that the Final Fantasy RPG/fighting game Dissidia, and its sequel Duodecim, can be played using D-pad instead of analog, an option that is switchable at any time. Plus, he game has, along with its brawling playstyle, a Command Mode, where you literally select commands from a small menu, like a classic FF game, and watch the AI make your fighter comply. This one needs less action and more thinking, which seems to be what you need.