You definitely need to keep a sanitizer in the water, because the last thing you want to add to the mix is an algae bloom!! There's no reason I can see why you can't go ahead and use your inline chlorinator. I've never repainted a pool, so I don't know if there's any "curing" process that has to happen, but you're going to have to keep some chlorine in the pool in one form or other, especially until you get some stabilizer in there, and since it's all just chlorine when it mixes in water, it doesn't really matter whether it comes from bleach or trichlor tabs.
When you aerate the water, it causes the pH to rise, which is part of the TA lowering process. Sounds like it's working out just like it's supposed to, just trust yourself and stay with the process!! One thing to consider, though--how much topping off do you have to do? If you take the time and trouble to lower your TA, and then have to refill frequently with high TA water, then you're going to be fighting a losing battle by trying to keep it low. Where did you keep your TA in previous years?
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