Deniz

I want to recommend the obvious G-Senjou no Maou, but looks like you already play that. If so, then perhaps you could try Ace Attorney franchise then seeing that both of Dangan Ronpa and Umineko take some elements from Ace Attorney itself. Other than that, according to VNDB Majikoi also had some battle of wits. Hope it'll be help.

It's pretty fun to see certain elements of it that were used by the later works of that team when they became Key.

I started to One Kagayaku Kisetsu e.I really love reading old stuff.And it gives the as same great taste as Kanon.

Umineko is this pretty much (it picks up after the first episode and goes enough places to figuratively dwarf a space opera). 
Danganronpa also comes to mind. It's basically a series in which a group of prodigious high schoolers are forced to kill each other and get away with it. The games have "Class Trials", which are basically minigame segments where you go through evidence and testimonies with the other students and solve murder cases. It's over-the-top, it's bombastic, it's stylish, and it's amazing.

The most prominent translated titles with some battle of wits besides the two AkabeiSoft2 classics are probably the Innocent Grey titles Kara no Shoujo and Cartagra. Not for the faint-hearted though.
Comyu might also fit the bill to a lesser extent if you count the conflict between Akihito and Itsuki.
Saya no Uta also has kind of a battle of wits between Fuminori and Saya against... the rest of the world?! Good but also not for the faint-hearted.
Hanachirasu might also fit because it's about a blood feud between two sword masters, but it's more about sword fighting. It's also quite flawed IMHO.

Strictly speaking, battle of wits is a rare story element.  Here are some VNs that contain the element to some extent, but in most cases it is only to a minor degree or in only one or two of the paths.
 
To some extent, Hello, Lady is a battle of wits... but the protagonist is mostly acting against unsuspecting enemies.
Ou no Mimi ni wa Todokanai is a more recent one made by AXL that does have a battle of wits in some of the heroine paths, but it isn't about battles of wits centrally. 
Sinclient has spy games, Iluminati, and stuff like that... and the protagonist is at the center of it all.
Semiramis no Tenbin has Ami... though she is all about manipulating people into various compromising situations.
Re;Birth Colony has a few battles of wits... mostly because the protagonist is a hacker using a false identity to live the good life and act as a spy for a cyborg loli yakuza who happens to be his adoptive mother.
Izuna Zanshinken has one serious battle of wits that builds up throughout that particular heroine path (the orange-haired girl's path).  It gets pretty gruesome though.
Ojousama wa Gokigen Naname... its protagonist is a black-hearted butler who will literally do anything to protect his ojousama and little sister from his mistress's sociopathic aunt.  I honestly recommend this one for you.
Reminiscence (the series).  The protagonist is a negotiator and as a result...  I do recommend you read the entire Akagoei series first though.
 
 

Umineko no Naku Koro ni has a battle of wits plot, and it's also very, very good (albeit long).

I think it's okay to play directly there because I think it's charage in the first place meaning there's no heavy plot that required you to read the sequel. Although I guess it could be fun though if you knew the events in the prequel (Da Capo 2), but in the end my suggestion just continue this.
About side stories, there's an option to unlock it directly although beware of spoiler though. My advice here would be just unlock the stories naturally if one want to avoid spoiler. Okay, so there's 5 stories with varied length and content. My comment here would be the first one was very important as it was the real prologue for Da Capo 3 if one treat Weather Vane as common route imo, the 2nd was a little romance with Aoi and quite long (1st and 5th side stories were longer though), 3rd and 4th was very short and just tell the stories of side characters (Tomoe and Elizabeth) respectively and most importantly reveal that Tomoe was a hardcore katana maniac XDDD. The 5th was very important to Da Capo 2 veteran because it was belated epilogue for the prequel itself set back at 12 years before Da Capo 3 event (2060, while for other timeline it was at 1950 -1951 at London and 2072 at Hatsunejima again).
That's all that I could gather here again. Oh, and Suginami was quite interesting that he never change in either at 2060 or 2072, then again he is one of the biggest mystery in Da Capo universe so it's useless to questioning that.

From what I've read of it so far (just got started with chapter 1) it would be most enjoyable with the previous two having been read first but so far it's done a pretty good job of setting up and explaining the way the Da Capo world works and previous events that have occured so I would say that yes, it can be read as a standalone title.

Spoilers for the game as a whole.
 
Spoilers for Sunao's ending
 

Semiramis no Tenbin is a great game, except for Sunao's ending (hers has issues if you like Ami).  I will say that you will see the ugliest side of Japanese societal structure in this VN though.
Suzukaze no Melt is an excellent game, if you just want some charage/moege stress relief. 
Tasogare no Sinsemilla... it has a few endings that approach the Tsukihime 'normal' ending in style, but other than that it is an excellent game.
Tenshi no Hane o Fumanaide is one of my permanent recommendations for all Vn lovers to at least try to play.
Evolimit is great... and it is significantly easier than Dies Irae.
Devils Devel Concept has a difficulty level approaching that of Dies Irae, so you might want to avoid it.
Subahibi has mostly bad endings, so you probably want to avoid it.
Baldr Sky Dive has gameplay.
Hapymaher is a first-class nakige with the single best soundtrack in all of VNs.
Irotoridori no Sekai is Favorite at its best, so if you liked Hoshimemo, you are pretty much guaranteed to like it.
Sakura no Mori Dreamers... if you can remain sane after the prologue, it is easy to enjoy.
Sakura no Uta has the same problems as Subahibi
Kami no Ue no Mahoutsukai has a huge number of bad and 'normal' endings.
Eien no Aselia is fully translated but it does have gameplay.  However, if you are willing, it is a first-class VN story.
If you start Grisaia Part 2, I recommend you immediately play 3 after, as it is immensely frustrating otherwise.
Mirai Nostalgia was the first Purple Soft game to earn my mostly unstinting praise.
Sharin no Kuni will probably split opinions here, but I enjoyed it immensely at the time.  The only question is whether it will fit you tastes once you begin to play it.
 

While you could enable 2.0 extra maps at 1st playthrough (I already tried it), it's still no matter if you enable it because it was only unlocked at 2nd playthrough. That's all I could elaborate here, and you could ask us if you need some tips there. Have fun.

hey hope you enjoy. if you need any help go ahead and ask away! ill help anyway i can.

Did you use save from some online source there? Because I'm sure that the first time you play Kamidori there's no option to unlock extra dungeon. If that's the case, I think you could just unlock the extra dungeon. But if it's your first time play Kamidori, obviously don't unlock extra dungeon there because the enemies lever were quite high (Around 90). Hope it'll be help.

Perhaps things like Koihime Musou, Yumina the Ethereal, Kamidori Alchemy Meister, Shin Koihime Musou.

It's been a while, but Autumn is kind of weird in a good way and should at least somewhat dodge tropeyness. I wouldn't necessarily call it light-hearted though... sigh.
The problem with your request is that the more towards the light-hearted side you go, the more archetypical characters in Japanese VNs tend to become (or perhaps you'll just be more familiar with said archetypes from other Japanese media. Hard to tell now that I think about it.) There'd probably be a better selection in Japanese... as pretty much always, rip in language barriers.

There's already enough good recommendations above. But let me recommend both of Tears to Tiara and Utawarerumono there. And if you want to read untranslated VN, play Soukoku no Arterial. Hope this'll be help.

Seinarukana or its prequel. Just lighthearted yuri rape
https://vndb.org/v26
https://vndb.org/v74

Yumina the ethereal and kamidori alchemy meister
 
yumina is closer to what youre looking for but kamidori has some nice gameplay. ^ ^ its my favorite vn with gameplay. hope it helps!

Sengoku Hime series
Sangoku Hime series
Madou Koukaku (no rape if you follow the true history route)
 

Eiyuu*Senki GOLD
Shin Koihime † Musou
Kikouyoku Senki Tenkuu no Yumina
Gensou Douwa ALICETALE
Akatoki