Kafka by the River is also related to missing cats (killed), ancient wars and something magical.
I loved Kafka by the River, but couldn't finish The Wind-Up Bird Chronicle.
Kafka by the Shore. It is very different from Wind-Up Bird even though there are cats in it.
I recommend trying Wind-Up again. The first ~100 pages are difficult to get through at times (the narrator is infuriatingly apathetic), but one you get past that, it's an incredible page turner. I liked Kafka a lot, but Wind-Up is his masterpiece.