I'm also in central Florida. It sounds like you want the pump and SWCG to make maintenance "automatic". Using tabs (Tri-chlor) exclusively drives ph down and sends your stabilizer (CYA) higher and higher over time, unless you are replacing water from anything other than evaporation. Higher CYA requires higher chlorine levels to sanitize and keep algae away. Check out the best-guess chart under Doc's signature block. No matter how you chlorinate your pool, tabs, SWCG, bleach, etc. you need to test and monitor these levels. If your chlorine to CYA ratio drops below about 1 to 10, your going to continue to be frustrated. You need to know your CYA level.

You don't need a bunch of stuff if you do get algae - just chlorine to get to shock level in the best-guess chart time and patience.

Yeah, if you have a noisy pump, fix or replace it. If you run your pump at the minimum to just turn the SWCG on, will it make enough chlorine with your CYA?