This may not be of help at your house but commercially I worked at a facility that found beerstone in a few of their tanks at one point. They implemented a practice of hot rinse, phosphoric acid CIP cycle (20 mins), Hot Rinse, Sodium Hydroxide CIP cycle (20 mins), hot rinse, check PH, cold rinse, check rinse water and tank wall swab both with ATP meter. If ATP meter reads "0" then you are good to go and sani as usual before next use. If ATP meter reads anything "1" or higher then give another hot rinse followed by another cold rinse and a second round of ATP meter checks. Rarely did you not get a "0" on the second check, if you even had to.
Do you have access to all this stuff? I assume no since you are posting on homebrewtalk about your at home conical. The reason I say that is to point out the importance of proper initial passivation, as well as regular re passivation (I generally do quarterly on commercial equipment being used 2-5 times a week), to prevent beer stone.