A TA of 96 ppm for a spa using bleach is way too high. Spas have more aeration, shallower depth, and hotter water temperature than pools so will outgas carbon dioxide faster. A higher TA has such outgassing occur even faster. The sticky on How do I use Chlorine in my Spa suggests 50 ppm for the TA level, but that is with 50 ppm Borates for additional pH buffering. Since you are unlikely to be able to get boric acid for the borates, you should try the lower TA but be careful to not have the pH get too high too quickly (i.e. you'll need to check it more frequently).
Why do you think a TA of 96 ppm is too low? Where are you reading that? You cannot use "standard" industry advice. It's either wrong or incompatible with the advice we give that is based on actual science.
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