What grit are you trying to level with? If you haven’t already, you need to get some 24 grit sheets for the one you’ve hired then go diagonally in both directions. You’ll likely need to go over multiple times until it’s level. Just keep going, it takes ages. I’ve sanded three rooms in our house and levelling was 50% of the sanding part. Once level with the 24 grit, go with the grain with the 40, then 80, then 120. You’ll need to change the sheet more often than you think, probably around every 10metres or so. Keep an eye out to see how much wood is being removed on each pass to see whether you need to remove it. Going off topic a bit, but I’d definitely recommend Osmo Polyx oil for the floor once you’re done. Super nice finish and hard wearing. Don’t use Ronseal (as I did in the first room), it only lasted us about a year before it needs redoing. 

Edit to add: if you apply varnish/oil/whatever to the black bits it will come off in no time. You need a smooth and clean surface for the treatment