I think you are doing fine.
Yes, your TA is high, and it sounds to me like you are performing that test correctly. The high TA won't be an issue as you know to monitor the PH. You are doing that.
Adding the acid in the amounts we recommend to keep the PH in range, won't harm you or anyone in the pool. That's why the process is gradual. Obviously adding all that acid at once would be extremely dangerous and detrimental so it's a slow, gradual process to lower TA. As I stated, there is no reason to rush it.
Pool School can be alot of information to try and absorb all at once. I've been there, so no worries. We'll help you gradually, one step at a time.
This is new fill water correct? It doesn't appear to me that you are trying to shock the pool... just maintain your FC level according to the CYA chart and you should be fine there.
Right now your main issue is daily testing of PH and FC, keeping them in range. 5-7 days after you have added the CYA, test to see where your level stands, and adjust your FC levels accordingly. Test the TA weekly while you are in the lowering TA mode.
Hope this helps - post back if any of this doesn't make sense.