On your pool, each fluid oz will add 1 ppm polyquat, using the 60% HTH product. A reasonable dose would be 2 fl oz (1/4 cup) every 2 - 3 days.

Add a dose, install the Unicel cartridge, leave your pump running, then stir up the pool, and see if the stuff will filter out.

Hold off on the HEDP - calcium that high makes the HEDP problematic. I working on that. Did you test the CH level & TA levels in the water in in the lime softening bucket? If that went well, (CH>100 ppm), the first step might be to run that on your pool.