Have you thought about using a scrub plane? I used one on my floor in a few spots, and now that it has been down for several years, I wish I had done more. Just make sure you go with the grain so you don't make chips.
Just set the plane so it takes very shallow furrows, and use it to level out any high spots. After finishing it looks a lot like some of the high end wood floors that called themselves scraped. You can see an example at
penningtonhardwoods.com/scraped.htm which I just googled using "scraped hardwoods"