Calcium Hardness (CH)
Because you have a vinyl pool and assuming you don't have anything fancy such as tile with exposed grout, then you don't need to worry about your CH and the 120 ppm is fine. Of course, you've already bought and added more which isn't a problem but was not necessary. 15 pounds of calcium chloride (anhydrous) would raise the CH by 95 ppm in your 17,000 gallon pool, so should be about 215 ppm now which is no problem.
Total Alkalinity (TA)
As for the TA, you can use
The Pool Calculator to calculate quantities though 70 ppm is not bad unless you were to use Trichlor as your source of chlorine. For bleach or chlorinating liquid (or even Cal-Hypo), a lower TA will help reduce the rate of pH rise. It takes about 4 cups of Arm & Hammer Baking Soda to raise the TA by 10 ppm in your 17,000 gallon pool. You can add this amount to get to 80 ppm.
Free Chlorine (FC) and Defeating Algae
One gallon of 6% bleach in 17,000 gallons only raises the FC by 3.6 ppm and even two gallons would be 7.3 ppm which isn't anywhere near what is needed to completely kill algae growth with an existing bloom. Bleach usually comes in 96-ounce jugs, not in gallons, and 1-2 jugs would raise the FC by 2.7 to 5.5 ppm. Algae grows and consumes chlorine even when it's not visible -- by the time it's visible the amount of algae is large enough to clump and reflect light. Before that the water could be cloudy, dull or even clear but still consuming chlorine. The way to get ahead of this is to shock the pool to kill all the algae by following the procedure described in The Pool School
here.
Pool stores do not always measure accurately and this is especially true with the CYA test that is critical to know. So IF your 35 ppm CYA level is accurate, then it would take 14 ppm FC consistently held to shock the pool and I'd just play it safe and use 16 ppm FC as a target. That means a LOT more chlorine than you've been adding -- it's about 4-1/2 gallons of 6% bleach or almost 6 96-ounce jugs and that's just to get the FC target -- it takes more chlorine to keep the FC level there until the algae is all killed. If there is a pool or hardware store selling chlorinating liquid at a decent price, then that would be less to carry. Bleach at $1.25 for a 96-ounce jug is equivalent to $3.38 for one gallon of 12.5% chlorinating liquid. I would lower your pH to around 7.2 by adding 2 cups of full-strenght (31.45%) Muriatic Acid (slowly over a return flow with the pump running) before shocking with a lot of chlorine. Chlorine should also be added slowly over a return flow with the pump running. In both cases, for extra safety, lightly brush the side and bottom of the vinyl pool where you've added chemicals to ensure thorough mixing.
Algae growth is one of those things that you have to get AHEAD of in order to get rid of it and then you need to MAINTAIN an FC level to keep it from coming back. In your case, I'd never let the FC level drop below 3 ppm once you've gotten rid of the algae. You'll know when you can lower the shock level of FC when three things occur: 1) you measure <= 0.5 ppm Combined Chlorine (CC), 2) you measure <= 1 ppm drop in Free Chlorine (FC) overnight, and 3) the pool water is crystal clear. The accurate FC and CC readings are one reason why a good test kit is the first and most important requirement.
Closing a Pool
Since you will be closing the pool you have other options. One is to get rid of the algae and be able to hold chlorine as described above and in the link to defeating algae. Then you would need to maintain chlorine levels in the pool over the winter. You didn't say whether it freezes where you live so it may not be practical maintaining chlorine levels over the winter. Some tips for closing an above-ground pool are given
here. Another option is to just let the pool go and clean up the inevitable algae mess in the spring. Though this sounds bad, it is something that can be done using bleach or chlorinating liquid alone as shown
here.
Richard