Evan's guidance is good.

I will add three things: 1) You said your pool bottom is gunite and flaking and your calcium level is 190ppm. That's below the suggested range of 200-400ppm. I suggest you raise it.
2) There is a little fountain for about $20 that screws into your return instead of the eyeball. It can raise pH at a PRODIGIOUS rate via aeration.
3) If you buy 12% Liquid Chlorine in 5 gallon carboys with a spigot you can use to pour off the LC, and just reuse your empty bleach bottles, you'll twice the "bang" from each bottle. Your only recycling will be to bring the empty carboy back to exchange when you get a new one.

There's nothing fundamentally WRONG with using Trichlor tablets IF you use them correctly.

Carl