Just. Wow. I hadn't realized it till I played this, but I had been missing being able to just genuinely enjoy a story with erotica content without reservations. I realize not many would sing the praises of the narrative here, but I couldn't leave it unmentioned. Mostly it's because I sit in a weird limbo of loving expansion content, but not really being invested in the extreme sizes that result, even though those are often the best expansions that I enjoy the most.
So I tend to end up consuming a lot of corruption and manipulation story content. As someone who really likes happy endings and pointlessly cruel people getting their consequences, this story was super refreshing. I hadn't completely realized how invested I was in the reading until it got to the part where Lucy got called out for her hostility, when it really sank in. That was a fantastic and fresh experience, the MC actually throwing out someone in the middle of the process for a completely sound reason, and not having some deus-ex-machina process allow the fetish content to power through via plot hole.
You've essentially re-created the psychology experiment of leaving people in a room with a button that buzzes them; Showing that a long enough, but often quite short, amount of time will have them so bored they start buzzing themselves, just to have something to do, and it was shocking them. Here, people are at risk of starving to death trapped in a isolated box, and the solution is not only pleasant, but being properly controlled and studied. It also hits reasonable snags in the process, with sane people managing the solutions. Your team has somehow managed to not only have the cake, but eat it too. Neither the story nor the erotica are isolated from each other, and I wish more stories or games could do that, hard as it is.
In addition, I don't think I've ever played a match game that took the power scaling approach used here. I was hyper skeptical about how long or effective the time limit always being 30 seconds could be, but I've fully consumed all the content and never once thought the game mechanics overstayed their welcome, even failing off and on. That's a great accomplishment, you've built a very sound gameplay loop for your purposes here. I'm a big fan of the approach that any games fail state should have the absolute fewest inputs needed between a fail and a retry, and that's very much the case here.
All around, absolutely well done.