There are apparently many who feel increasingly annoyed (unfortunately, this seems to be leading to an ever-increasing level of xenophobia, which I find very disturbing). I am not among them. If anything, I would say that Kyoto (supposedly the most over-touristed place in Japan) has become a value destination, because so many hotels have opened in the last five or so years. If you go outside the busiest seasons/holidays, hotel rooms there, especially single rooms, are a real bargain. Furthermore, if you simply resist the pull of the tourist magnet sites, you can easily find the qualities that have long made Kyoto one of the most amazing cities in the world. Why in the world do you have to go to Kinkakuji? Sure, it's a pretty picture, but there are countless sites in Kyoto that are at least as good (far better, if you ask me). I haven't been to Kiyomizudera for years and am perfectly happy not to ever go again, because I have my own favorite places in Kyoto that are generally deserted, and every time I go I discover new ones. I guess it is hard to say good-bye to a place like Fushimi Inari Jinja, but I have found so many other wonderful places that I have no regrets. In fact, I am really grateful for the tourist magnet sites, because they suck up all the tourists! Just avoid them, and you will find very few tourists. It's as easy as that.
As for Himeji Castle, I was there last June and when I went it was not crowded at all. I wouldn't go in April, or any time on a weekend, but I went on a weekday about an hour before they closed the gates for admission (which gave me more than 90 minutes inside, which is certainly plenty), and lots of people were coming out but almost nobody was going in. Then the next day I went to Kokoen next door when it opened in the morning, and had several of the subgardens completely to myself for close to an hour. It was just amazing. A lot of places I visited last year were like that.
If you love Japan, then just consider going beyond the famous tourist sites. The country has so much more to offer, and what you are looking for is still very much there. Also, if you can go during less-busy times (for example, late May or early June, or February), you will have a lot fewer people to deal with.