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.