If your pool is overfilled, like after a storm, you can vacuum to waste and kill two birds with one stone. Otherwise, I vacuum to filter and empty the pump basket right after.
I would bring your FC up to slam level for your tested CYA with liquid chlorine (bleach or liquid shock ) and hold it there for 24 hours and then see if you can pass the OCLT test as your first goal.
I have found that if u keep up the slam for 3-4 days with your pump on recirc, then vacuum to waste before switching to filtering produces the quickest results with the least amount of filter backwashing. YMMV.