I use PCO as my go to finish. You are not on the wrong track. Put three coats on. Level sand....dry. You are not trying to sand to wood. Just leveling out the highs and lows of the finsih. When the pores disappear you are ready to put on the top coats.
I use 320 to level sand. You are correct that 600 doesn't give enough "slurry" for filling pores. Since you are at that 600 level now. Going backward is counter productive. One may use the finish to build and fill pores. You just have to be patient. The can says 6 hour dry time between coats. I prefer a little longer. After 3 coats, I will let the finish set 24 hours before I level sand. I suggest you tape off your checkering. It will save you hours of labor later on.
