Suikoden. The first game is a tight, heavy war story with lots of major character deaths and no ergregious animeisms. You also get dozens of party members to mix from, so you assemble your six man party of your favorites.
If you like that then play the second game, though it is not quite as good as the first one story wise as there are less deaths and they are stretched out across 40 hours instead of 15. It has the more likeable cast of characters, though. If you finish that and still want more, then play Suikogaiden and then Suikoden 3. Suikoden 3 however is where the series creator Murayama left and the series begins indulging in JRPG tropes like fighting the same supervillain multiple times. If you want even more Suikoden after that, there is 5, which is overall a little more lighthearted than the rest of the series and feels the most like a regular JRPG, though it is still about a war and has some deaths. The first two games and Suikogaiden have good music by Miki Higashino.
Next is the
Tactics series, most famously Final Fantasy Tactics which is grossly overrated but still decent. My personal recommendation would to play either Tactics Ogre, or Ogre Battle 64. The problem with FFT is that it starts out being about unpaid war veterans during a bad economy forming a rebel army to get their pay so they can buy food, but then the plot quickly gets hijacked by demons and becomes about le evil church. Tactics Ogre is people vs people almost all the way through, with it only the JRPG demon monster showing up at the very end as a victory lap. Tactics Ogre also feels more war-like as you can field 10 characters at once as opposed to FFT's only 5. Ogre Battle 64 has nice looking backgrounds and sprites, and has RTS combat and feels like you are managing war with multiple different squadrons rather than just 5 to 10 guys, but the story isn't as good as Tactics Ogre's.
The Last Remnant's gimmick is that it is a JRPG where - rather than controlling a party of 4-6 characters - you instead control up to 5 parties on the battlefield at once (the maximum number of characters you can field is 18 characters, so you can either have like 2 parties of 5 and 2 parties of 4 for a set up of 5/5/4/4, or you can do something a little riskier like 4/4/4/3/3).
Don't play this game for the story. I clocked 100 hours, and maybe 1-2 hours were cutscenes. TLR is 50% battles, 20% setting up your party in menus, 20% reading a walkthrough/the TLR wiki, 8% running to the next battle, and maybe 2% actual story. Seriously, this game is about gameplay. If you want a story heavy game, go play Trails or Final Fantasy. The story held some promise during the first 10 hours, but then that all fell by the wayside as it became all battles, and the story was rather... meh.
I strongly recommend using TLRPlanner, a cheat app that allows you to just force spawn quest mobs, and force drops every item in a mob's loot table upon death, so it minimizes the amount of reloading you need to do.
The power metal battle music is very nice to listen to.
Ring of Red is an SRPG set in an alternate post-WW2 timeline, where Germany began developing mechs during the late stage of WW2. It wasn't able to stop the fall of Germany, but the proliferation of mecha altered the timeline so that Japan was split into two by the Allies and the Soviets. 15 years later (I forgot exactly how long), a prototype super mech is hijacked from the Allies by some guy who returned to North Japan after having fought in Korea or Vietnam. Your South Japanese mecha brigade is disavowed by the Allies (while still actually working for them) and crosses the border North to recover or destroy the super mech. After 30 hours the gameplay became very repetitive, even with turbo mode.
Final Fantasy XII is the last of the super serious JRPGs that I have played. It has good aesthetics and - up until the very end - the story is about geopolitical conflict and the dispiriting reality of a long and unrewarding insurgency. Sadly the creator Yasumi Matsuno quit during development, so the game is unfinished and has an abrupt, uncharacteristic JRPGy conclusion that the story did not feel like it was heading towards. The game has a lot of optional bosses you can fight if you want a challenge. The weakness is that the main cast of playable characters are very dry, and I wish the more lively side characters had been my party. Also, it has unflattering RTWP combat without the spectacle and the presentation of the other FF games. Play or emulate the original PS2 version, as the so-called "remaster" washed out the textures.
If you are willing to tolerate some lighthearted JRPG stuff and tropes, then I would recommend looking at Valkyria Chronicles 1 and 4, Aselia the Spirit of Eternity Sword, Trails in the Sky FC, and the first two Trails of Cold Steel games. They are JRPGs with a story about geopolitical conflict and can be a little more moody/realistic than your typical JRPG. I know you dismissed ToCS1, but ToCS2 has an unexpected final act. I guess I might also recommend Fire Emblem. I know that Fates is often maligned, but I thought the finale of Birthright was poignant. FE4 was hyped up as this masterpiece, but when I played it I found it to be disappointing.
Valkyria Chronicles 1 & 4: a third person shooter/SRPG set in fantasy WW2. Is made by the same devs who made Sakura Wars and builds off of SW5's gameplay. Good missions. Good soundtrack and aesthetics. VC4 starts off somewhat animeishly juvenile but then becomes serious and eclipses VC1 IMO, and has better levels than VC1. Overall the better game of the two.
Aselia the Spirit of Eternity Sword: visual novel/SRPG hybrid with some grand strategy elements. You and your little sister get isekaied to a medieval fantasy world and are promptly captured and enslaved by the local kingdom. You are then taught their language and blackmailed/coerced into helping conquer the adjacent countries. The main character gets bonded with a demon possessed sword and faces temptations and crushing guilt. This game is very, very hard and you will need to save scum a lot. You may also need to use a window resizing program to get the game to fullscreen properly on modern displays (I forgot the name of the one I used). Has a fantastic soundtrack by Aki Hata.
Trails in the Sky FC is set in the wake of a war between the Kingdom of Liberl and the Erebonian Empire. It starts off being about adventurers, but then becomes about
a military coup within Liberl's military that is trying to prepare the country in the face of the escalating cold war between Erebonia and Calvard and the inevietability of a world war and another invasion.
Trails of Cold Steel 1 & 2: is set in fantasy Prussia at the beginning of the modern period. There is turmoil within the Erebonian Empire as industrialization is happening and the state is consolidating power, stealing wealth and power from the landed aristocracy and trampling commoners in the process. There is also a brewing cold war with the villainous Republic of Calvard in the background. The first game alternates between slice of life fun at school, and field trips to a town in the Empire where the protagonist gets entangled in the turmoil encompassing the country. The first game then climaxes
with a war against Calvard, a bank crash, and civil war within Erebonia. The second game is about
the civil war within Erebonia and then touches a little upon the war with Calvard. If you enjoyed the game and want more, then play the sequels, though they drop the more realistic and bittersweet outlook that the first two games had and goes for a traditional JRPG "friendship overcomes anything" tone. Has a fantastic soundtrack.