I think secrets are a very positive thing; they can add depth and make the experience more memorable. But in my opinion, the main story should be solid and consistent. If the secrets reinforce the tone, expand the lore, or add interesting layers, they will greatly enrich the game. If they feel disconnected or too big in relation to the main plot, they can dilute the overall impact. First, a strong foundation, and then secrets to enhance it.
I am also developing a fairly long game and encountered the same problem: I had a very defined and powerful main story, but also lots of ideas for puzzles and small plots that, at first, didn't quite fit. In the end, I decided to integrate them into the main narrative to provide coherence and make everything part of the same universe. It wasn't easy, and I had to discard or adapt several ideas, but I think the result will be much more satisfying than if those subplots had nothing to do with the central plot. Sometimes it hurts to cut or restructure, but when everything points in the same direction, the whole thing gains a lot of strength...