Having gameplay before you reach the lewd content is what separates games from just a picture gallery search, I think it's important to keep at least some semblance of puzzles in the game. That being said, I'd much prefer the "one turn to checkmate" ones over the "two turns" ones, because the first is fun and accessible for everyone but the second requires either annoying trial and error or a more chess-savvy orientation.
Also, the sandbox is cool and I'd love to see more content, but it does feel a bit grindy having to check every single room at every single time of every single day just to check if there's anything different. Perhaps adding something like a character map, or an event list with hints, or something to better and easily know if there's anything new to do at all in that specific weekday, would alleviate the experience and make it more streamlined like some of the pure sandbox games out there.
I really like HSDXD and I think this game has potential to be the best lewd tribute to it, so I'm really rooting for you. Keep doing mostly what you've been doing so far and it's going to be great.