The key will be bringing your chlorine to shock level and consistently keeping it there. With a 60CYA you need to keep the chlorine level above 20ppm. You should get a K-2006 test kit so you can know for sure where you are at chemical wise. PoolDoc wrote up a helpful post about how to get the right kit: http://www.poolforum.com/pf2/showthread.php?14994

If you can test and add chlorine several times a day, that will probably help. Make sure you're running the pump/filter 24x7 while you clean things up. The chlorine kills the algae, and the filter removes the dead algae from your pool.

Without the K-2006 kit you can't say precisely when you're done killing algae because you don't have a combined chlorine reading. However, you should at least keep shocking until the water has been totally clear for a day or two. Also, I might be misjudging your filter but I'd probably be cleaning it daily rather than every few days while you clean up.