I would add chlorine even if you're starting the SWG soon. Best to keep it at that minimum level just so that no problems develop now that you're so close. What's a jug of bleach cost, after all?
TA by itself isn't a big deal, but it makes it more likely that your ph will rise in the future. Not sure if TA, affects the SWG though, so might want to get that under control before turning it on.
It is important to always keep your chlorine level above the minimum level for your CYA level to keep your pool sanitized and stop algae from growing. Chlorine CYA Chart
Nothing wrong with lowering TA, but I would be inclined to give the pool a month or so to get settled in and see how PH behaves.
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