Actually, if you lower it AS you fill it, and arrange for your fill water to 'splash' into the pool (aerating it) you will strip quite a bit of carbonate alkalinity before you even get it full!

By the way, you do want to follow the "lower it to 7.0, and then add one more dose of acid" method. You test kit almost certainly can't distinguish 5.0 from 6.8, and a pH of 5.0 will damage things. However, if you lower it to the lowest distinguishable level (just above 6.8) you can add one more dose of acid and be pretty sure you haven't gone lower than 6.5.

Ben