Part of the problem here is that 時をかける少女 isn’t a light novel. I don’t think it’s technically a kids book, but it’s much closer to a kids book than an adult-targeted novel or light novel in terms of kanji usage. I think what you’re experiencing is pretty normal and I’d guess that most Japanese learners who learn a lot of kanji experience this at some point. That said, I agree with @downtimes that reading words in kana “simulates” listening practice in a sense, so if you can’t recognize a word in kana it probably means you don’t know the word well enough. But if you want to read a book with more “normal” kanji usage, you’re definitely better off reading an adult-targeted novel or an actual light novel.
Specifically, if you want to read a standalone novel I’d recommend かがみの孤城. It has normal kanji usage but is on the easier side, so I think it’ll be good for a first book (or second if you finish 時をかける少女). There’s a book club which is currently about halfway done the book (which was split into two parts, so we’re nearly done the first part). I already finished the whole book and loved it. かがみの孤城 (Kagami no Kojou) Book Club
If you want to check out a longer light novel series I’d recommend 本好きの下剋上. I think this is also on the easier side, but it’s slightly harder than かがみの孤城 in virtually every aspect of the language. There was also a book club for this for the first three books, along with a discussion topic for subsequent volumes. I’ve read the first 14 books so far and it’s very consistently enjoyable. 本好きの下剋上 home thread