Re: Nature 2, BBB Method and KIS
The answer on the bleach vs Tri-chlor comes down to testing. If your pH is good and your CYA is where you want it, don't use tablets, regardless of the time of year. If your CYA is low and your pH is a bit high,then by all means you can use Tri-Chlor. Bleach doesn't affect CYA, pH, TA, or CH. You can adjust pH separately with Muriatic or Dry Acid to lower, Borax to raise. You can increase CYA by adding CYA powder.
Tri-chlor tabs can be CONVENIENT but aren't necessary.
Re: Nature 2, BBB Method and KIS
I don't believe you understand how insidious Trichlor tabs can be. The following are chemical facts independent of concentration of product or of pool size.
For every 10 ppm Free Chlorine (FC) added by Trichlor, it also increases Cyanuric Acid (CYA) by 6 ppm.
For every 10 ppm FC added by Dichlor, it also increases CYA by 9 ppm.
For every 10 ppm FC added by Cal-Hypo, it also increases Calcium Hardness (CH) by at least 7 ppm.
So with a typical 2 ppm FC per day chlorine usage, Trichlor tabs will increase CYA by 36 ppm PER MONTH. They are of course fine to use if you are low in CYA and intend for it to increase or if you are going to use them for a shorter period of time (say while on a week vacation), but you really have to be careful not to overuse them. I doubt very much that you would be able to use them for an entire summer season unless your season is short (that does not sound like your situation) and/or you have significant summer rain overflow to dilute the water.
Though I know what happens to the HEDP-based metal sequestrants we normally recommend (when needed), I do not know what happens to the acrylic acid copolymer, but it doesn't look like it's a molecule that breaks down very much from chlorine. I don't know if there are any tests for it (you can contact Jack's Magic to ask them both questions -- what happens to it and can its level be tested). I will say that polyacrylic acid (PAA) which it may contain will produce a precipitated mess if you were to use a cationic clarifier (most pool clarifiers are cationic). That's one reason we don't recommend using it.