According to the "best guess" CYA chart, at 70ppm CYA, you need to maintain at least 5ppm of free chlorine in order to properly sanitize your pool:

Stabilizer . . . . . . Min. FC . . . . Max FC . . . 'Shock' FC
=> 0 ppm . . . . . . . 1 ppm . . . . . 3 ppm . . . . 10 ppm
=> 10 - 20 ppm . . . . 2 ppm . . . . . 5 ppm . . . . 12 ppm
=> 30 - 50 ppm . . . . 3 ppm . . . . . 6 ppm . . . . 15 ppm
=> 60 - 90 ppm . . . . 5 ppm . . . . . 10 ppm . . .. 20 ppm
=> 100 - 200 ppm . . . 8 ppm . . . . . 15 ppm . . .. 25 ppm

Your problem is those pucks that contain stabilizer - it keeps building up in the pool. To avoid the problem only use unstabilized chlorine (such as plain unscented bleach) and add CYA separately as needed (once a season probably). I don't understand why you are getting no Cl reading with your high level of CYA it should not be burning off by the sun. Hopefully others will have some ideas on this.

~Rick~