Stat-raising otome vns are a bit of a controversial subject. I won't lie, I mostly find them to be frustrating, because I'm a completionist and I always try to achieve the perfect outcome/ending. Games like Long Live The Queen are not very fun for me, because I either need cheats or I can't finish the game the way I want. Don't get me wrong, I actually love that I can get bad endings, and while I agree that you shouldn't lock LIs behind certain stats, I still think that you should seriously consider adding bad endings to the game, because they make getting the "golden ending" much more rewarding.
A good example of a stat-raising otome done right is Seven Kingdoms: The Princess Problem. It's only a demo right now, but it's the first stat-raising game where I actually have (a lot of) fun playing, because it has a great balance between frustration and gameplay.
Have you considered an approach similar to The Royal Alchemist? Like LLTQ, you can die a lot, but every time you die you gain a bonus to your stats, so you can, eventually, succeed all the skill checks if you play the game enough times. That was a great idea because it adds replay value. Obviously I don't think this is the sort of game where we die a lot, but a new game plus would still be nice.