HHHmmmmm, didn't think about going the city route, I don't think there would be a problem as the previous owners kept records for almost everything in the house and Im pretty sure they got a permit for it.
Yes to do it the diluted cya test we would still use the tube you just want to use half pool water have tap water to start with. Odds are that draining half at the same time will not be a problem. But there's always a small risk. Although since we don't know how high your cya really is even a 50% drain may not be enough and you might have to do it again.
Question around testing cya? Can you just use half pool water and half tap instead of using the chemical that comes with the Taylor kit for the black dot test?