Not exactly obscure, or unpopular, but:
Wild Arms XF:
A strategy RPG that has a class system that is a bit more Tactics Ogre than FFT. It's known to be pretty difficult, but really it's just that many missions have objectives other than just "Kill all the bad guys" and that grinding isn't very rewarding early on. Wild Arms is a long running series on the PS1 and PS2, but each game is set in its own version of the world. Knowledge of the other Wild Arms games is not needed here.
Valkyria Chronicles 2 (and 3!):
Valkyria Chronicles is a tactics game where you make decisions on a large map, and then take direct control of the unit in a semi-realtime 3rd person shooter during their turn. Your squad members have somewhat set classes, like in Fire Emblem, but different stats and strengths in those roles. The setting is an analogue to World War 2 in the European Theatre, but in a Shonen Anime world. VC2 takes place directly after the original Valkyria Chronicles (available on PS4, PC, PS4, Switch) and definitely has some spoilers for that game. VC3 is fan translated, and takes place during the events of the first game. Expect at least a few spoilers here too.
The Legend of Heroes: Prophecy of the Moonlight Witch, A Tear of Vermilion, and Cagesong of the Ocean:
Three separate RPGs in the Legend of Heroes lineage. If you've played any of the Trails games, their style pretty much starts here. That is kinda way overselling these three though. These are PSP ports of RPGs that came out on Japanese computers in the 90s. The strengths of the original games were their tactical combat systems (gutted in the PSP ports) and their in depth, personal stories (kinda ruined by a bad English translation.) The US release order is also weird, with Tear of Vermilion released first, despite being the second game. These games are part of the long running Legend of Heroes series (itself part of the longer running Dragon Slayer series) but this trilogy stands on its own apart from the previous LoH games, or the later Trails series. If you want to see what the Trails series was building on, or have the patience to sit through some Kemco style RPG design, you'll probably have fun with these.
Ys Seven:
The Seventh entry of the Ys series. No longer a PSP exclusive. It's an action RPG with multiple party members who have different strengths and fighting styles. Ys is pretty well known for its speedy action, and intense boss fights, and Ys Seven delivers pretty well. Each Ys game is a pretty much stand-alone adventure, except for the first two, which are pretty much always packaged together. You don't need to have played other Ys games to enjoy this one, but there are a few returning characters. If you do want to play other Ys games, YsI & II, Ys: The Oath in Felghana (a remake of Ys III), and Ys Origin are also available on PSP. The PSP port of Ark of Napishtim (Ys 6) is not great though. You'll need a Vita, or PC to play the remake of Ys 4, and you'll have to wait with the rest of us for a remake of Ys 5 though. (or bust out the SNES emulator)
Star Ocean First Departure:
A remake of the original Star Ocean on the SNES, using the engine of Star Ocean 2. It's an RPG with a real time combat system, similar to the Tales games. It also has an in depth character skill and crafting system. The Star Ocean games kinda sell themselves as sci-fi stories, but most of SO1 takes place entirely on a planet that looks very much like a generic fantasy RPG. This has been ported to the Switch as well, but not to PC, so the PSP version might be more accessible. The PSP port of Star Ocean 2 is inferior to the recent Second Story R remake in pretty much every way though.
Metal Gear Solid: Portable Ops:
I know you said no MGS, but, Portable Ops is definitely unpopular. Basically an MGS game made with very little oversight by Kojima. It takes place between MGS3, and MGS: Peacewalker. Peacewalker is a more traditional MGS experience, but Portable Ops really focuses on recruiting the right soldiers for the job, either by having the right skillset, or by previously being part of a unit that is prevalent on a map. Basically, if your guy has the same uniform as the enemies, he can walk around more or less uninterrupted. You also need to manage stamina between your units, so unlike Peacewalker, you can't really just use Snake for everything.
Tactics Ogre: Let Us Cling Together (with the One Vision romhack)
I am personally more of a fan of Tactics Ogre Reborn. If you need an introduction to the game, it's basically the less appreciated older brother to Final Fantasy Tactics. You can't do as much class mixing shenanigans, but all of the strategy, the mature storytelling, and the war crimes are on full display. The One Vision romhack is a rebalancing of the game, and is really the only reason I would suggest the PSP version over Tactics Ogre: Reborn. If you want, you can even spin up an eBoot of the PS1 version of the game, and enjoy entirely different gameplay and a janky translation.
Brandish: The Dark Revenant:
Brandish is a kinda weird series. It's kinda a top-down action RPG, like Zelda, but with the logic of a first person dungeon crawler like Wizardry. Your character always faces forward, which means when you turn, the dungeon turns around your perspective, rather than the map staying static and your character moving. I have read that the PC versions of the Brandish games are snappier, and have a screen layout that makes this make sense. The SNES versions of Brandish and Brandish 2 really just induce motion sickness for me though. This is a port/remake of the original Brandish, and while it still has the odd movement, it feels better here than the SNES version. The game also has a second quest as an alternate character after beating the main game.
Final Fantasy IV Complete Collection:
Final Fantasy isn't unpopular, I know. This is one of the better versions of FF4 though. The main FF4 game here is based on the GBA port of FF4, which means it includes the bonus dungeons and the ability to switch your endgame party. The collection also includes all of the chapters of The After Years as they were originally released, as opposed to the WiiWare version which combined Ceodore and Kain's chapters. You also get a little interlude chapter between FF4 and TAY, but it's not exactly riveting.
Lunar: Silver Star Harmony
A remake of the PS1 version of Lunar. Lunar is a pretty traditional JRPG with anime cutscenes and voice acting. Each member of your party has a set list of skills and abilities, so there isn't really a party building element here. Lunar is the kind of game you play for the story. I personally prefer the PS1 version of Lunar, and there is a more recent set of remakes of Lunar and Lunar 2 available on modern systems. I don't think that Lunar remake is based on this one. That does mean this version has a unique Prologue section with the 4 heroes, which is neat.
Literally any PS1 game:
I know you came for PSP game recommendations, but the truth is that when I had a PSP, and had hacked it, I used it almost exclusively as an emulation device because of how well it could emulate PS1 games. If you have a physical PSP and aren't just emulating it, slap on some PS1 games. Some of my favorites to play on the go were Parasite Eve, Vanguard Bandits, Vagrant Story, Legend of Dragoon, Xenogears, Suikoden, Suikoden 2, Wild Arms, Wild Arms 2, Ogre Battle, Vandal Hearts, Legend of Mana, the PS1 Final Fantasy games, etc.