You've played RPGs but you haven't played Chrono Trigger? Wow, that's messed up.
You really need to play Phantasy Star 1, it was so far ahead of its time that it's amazing that it isn't a name everyone knows.
For SNES games not mentioned in your list I'd recommend some of these:
-Terranigma: From Enix, in the relatively identical style of Illusion of Gaia and Secret of Mana series. I've heard a rumor that it was its very Pagan and evolution-supporting storyline that kept it out of America. However, I'm not sure how PSP emulates the SNES, but the game is in PAL screen format and may require computer use (it was never released in North America)
-Paladin's Quest: Pretty good game, I don't know why it isn't talked about more
-Bahamut Lagoon: You need a translation hack that can be downloaded online. If you've played Seiken Densetsu 3 or Final Fantasy 5 then you're aware of the process.
-Star Ocean: Same as Bahamut Lagoon, you need a translation hack.
-E.V.O: Search for Eden: Not exactly an RPG, but it's sidescroller journey through evolution and time. You get stronger by spending points to evolve new/better parts. Made by Enix and the story is similar to that of Terranigma.
You can PM me if you need some help with the hacks.