The rates are so high because it's peak travel season in Kyoto, even more than cherry-blossom season.....availability does tend to vary though. I've been there a few times in November and have seen it showing sold out when looking early but rooms did become available closer to the dates. Rates were high everywhere and didn't really change that much. $1000 is a bit excessive, those are more RC rates. I also have a trip planned at the end of November, I'm seeing guaranteed availability for JPY 40.000. That's not so bad since when there is availability the rates are often higher at around JPY 45.000. Weekends tend to be expensive....

You can easily visit Kyoto from Osaka, but personally I would still try to stay in Kyoto. Staying in Osaka the night before/after is an alternative.
I'm also fond of staying at the Granvia Kyoto. A little less luxurious than the HR but the location is perfect for me.