As it is a flat bed you can use a brand new Stanley knife blade to scrape across the surface, at a fine angle not like a scraper, and lift off the tiny rust nodules, after oiling. Bit like shaving. It might be a little hazardous if you are not steady handed.
Then perhaps a small brass wire brush, making sure it is brass not plated steel. Then the scourer, by hand. You would have to thoroughly de-oil to use a liquid (phosphoric acid) anti rust. Also avoid wirewool unless the ultra fine variety but that is still a scratch risk probably more cosmetic than damaging.
As you have probably run the saddle up and down to 'test it' you should remove same and clean the bearing faces underneath as they will have picked up some rust aka grinding paste.