I'm not sure that the algae is dead, dead, dead yet, so letting the chlorine down to zero may be a little early. Visibility is not close the bottom yet, and any results have only come along over the last couple of days with consistent high chlorine levels. I'm not sure what benefit their is in letting the chlorine drift to zero and putting in algaceide. From what I understand, teh aglae got going from yo-yoing chlorine levels.
I'm just going with my experience, but I kept the chlorine levels very solid until I was reading zero CC for a couple of days and was starting to see the bottom of the pool through the fog.
Until the CC is zeroed out, backing off the chlorine may not be the best bet and I'd err on the side of caution.
RR1953, if your kit doesn't give you cc levels, can you get it tested at a pool store? If they wonder at the chlorine levels, just tell them you are zapping a bunch of algae and ignore anything else :-) ! That cc reading is a good thing to know now.
Bookmarks