You can add stabilizer 3 ways:
1. Use a stabilized chlorine, like trichlor tabs or dichlor powder.
2. Use the liquid stabilizer -- 1/2 strength; 2x the price.
3. Use granular stabilizer BUT it's slow to dissolve so you MUST get your water clean first. Otherwise, you'll have to clean your filter and dump the stabilizer before it dissolves. You have to allow about 60 hours of circulation time to dissolve the granular stabilizer. If you have a pump timer, this can be 10 days!

Unstabilized chlorine has two practical forms: bleach, and cal hypo. Bleach is fine with hard water, but you'll have to tote a lot of bleach. Cal hypo will ADD hardness, if you use it according to the label instructions. There's a way to use it that will tend to REDUCE hardness, but it would be tricky with a cartridge filter.

What you might want to look at is getting a 50# container of diclor from Sams Club (NOT Costco!) for $105. At that price, it works out to be about $4.50/lb as 100% chlorine gas . . and about $5 lb as stabilizer. 6% bleach is costs about the same, on a 100% chlorine comparison, but does NOT include stabilizer. Dichlor is completely soluble, so you don't have to mess around trying to dissolve it on your filter.

You will have to switch to bleach or cal hypo at some point, because your stabilizer level will keep climbing. And, you'll need the K2006 testkit to manage both the hard water and the stabilizer / chlorine ratio.