Doki Doki True Route is an incredibly long but nevertheless unfinished mod. Sadly it looks like it will never be finished, since the last update was 9 months ago (as far as I'm aware). Still, I'd say it's worth playing. It starts with Act 1 of the original game, and your objective is to convince Monika to not delete Sayori. The first change you'll notice is that you have the choice to write poems for Monika. It actually took me a couple tries to figure out how to play my cards to make Monika have a change of heart, so I'll spoiler the solution incase you'd like to figure it out for yourself. Write all your poems for Monika, and ask her for help resolving the argument, but every time she asks you a question about Sayori, pick the more Sayori-favoring option. Eventually Monika will help you save Sayori and then delete herself out of shame. Wait for Sayori to prompt you to bring her back, and once you do, make sure you tell Monika that you love her, otherwise she'll simply delete herself again. After that, you'll find yourself in an alternate future where Sayori is the club president, and you must help her and Monika save Yuri and Natsuki from their problems.
As far as the secret-keeping thing, this mod avoids the moral perversion by giving a reason for it: the more characters know the truth, the more the game starts to break. So that's very good news.
I also like how the mod handles Natsuki's dad, turning him into a real character with a .chr file! (And he has a real name.) I do think his cruelty was a little overplayed from how it needed to be (this video is what I consider the ideal portrayal of Dadsuki), but it wasn't terrible.
My biggest criticism is that once you get into the main part of the game (post-restoring Monika), the poem writing and sharing becomes incredibly repetitive and boring. I'm not even sure if any of your poem choices matter at that point (I know the last few don't). And after saving both Natsuki and Yuri, the day structure becomes the same way, to the point where the last 5 or so days of the game all seemed like the same day repeating. I was soooo ready for the plot to just move on already.
Another criticism would be that it's a little unbelievable how obvious Sayori is able to make it that she's hiding something without MC and the others getting suspicous enough to press her about it.