Sounds pretty normal to me, for chlorinating a slimy pool. The alkalinity is NOT too high; don't worry about it. I'm a little concerned about the missing CYA; that may be a problem, but we'll find out later.

Meanwhile,

1. add a box of borax, to kick the pH up -- in case the CYA is missing and the pool has ammonia. Things go better at a higher pH in that case, and won't go worse
2. watch your filter pressure; Pleatco cartridges aren't the best, and if you let too much pressure build up, it will damage the cartridge.
(Clean it, check the gauge, and then clean it AGAIN when the pressure has increased 6 - 8 lbs. Do NOT let it increase more than 10lbs!!)
3. Polyquat will help filter the algae.
4. Add 2 gallon doses of plain 6% bleach each evening if the FC is below 10 ppm. BRUSH the pool after adding the bleach.

Otherwise, just keep going.

You may want to check and see if you have access to a Sams Club in your area that carries PoolBrand dichlor. They have it at my wholesale cost, and if you need to chlorinate AND add CYA, that's very inexpensive way to do it.

I understand the concern about chemicals, but if you are using the things you need right now -- bleach, borax, polyquat -- you are WAY safer at the pool messing with those, than you are doing your nails! Human toxicity of those three is quite low -- even if you eat them, but do NOT do that !