You are right that your CYA may be higher than 100. 100 is the upper limit on the test range so it might mean 100 or it might be any number higher than 100.
Janet (Aylad) does purposely run a HiC2 (high chlorine, high CYA) pool for the very reason you state. Living where it is super hot, allows her to not have to add chlorine every day. Whether this is for the reason you are hoping or not, this is what you are going to have to do by necessity due to your extremely high CYA. Covering your pool will also help the chlorine last longer between doses because it will cut down on loss to the sun.
The question is whether or not to continue to use the trichlor tabs. How many tabs do you have left and are they wrapped or unwrapped? If they are wrapped, I would probably not use any more now but save them for maybe next season. If they are unwrapped, that presents a whole other issue. Read this to see some of the discussion that we have been having recently about storing chemicals:> http://www.poolforum.com/pf2/showthr...-and-chemicals
One caution --- you need to be really careful that you do not get algae. In a HiC2 pool, cleaning up an algae bloom takes extremely high chlorine levels. http://pool9.net/cl-cya/
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