You do realize that muriatic acid will LOWER the pH. Also, when you add bleach, the pH goes up, but then back down once the bleach is consumed.

If you have access to a Sams Club, you can get their PoolBrand dichlor in either their 24lb box of 'shock' bags OR their 50lb bucket. Each pound of dichlor will add about 7 ppm of chlorine, and about 6 ppm of stabilizer. So, I'd recommend the 24# box, which will push your stabilizer too high. But, the bags keep in storage over the winter better than the bucket will.

Otherwise, any brand of stabilizer (so far, they haven't begun playing games with what's in containers of stabilizer!) will do -- 4 lbs, hung in a sock in front of a return, should do.