What can be done to bring the counting of divorce back to zero, even if the couple reconciles verbally and physically within the iddat period.

The divorce is valid and since you reconciled within the Iddat period there is no need for a new Nikah. (Ahsanul Fataawa vol.5 pg.153; HM Saeed)

There is no need for you to erase this divorce because you are still legally married. If your husband gives you another divorce, it will be counted as the second divorce. You cannot bring the counting of divorce back to zero, unless your marriage goes through the laborious process of analysation. This simply means that your husband will have to give you 3 divorces, after which you will have to sit in Iddat (in your case 2 more divorces as one has already taken place). Thereafter, you will have to get married to someone else and the marriage has to be consummated. Thereafter, this second husband of yours has to give you 3 divorces, after which you will need to sit once more for the whole Iddat period. Once this has elapsed, you can now get married to your first husband and now your counting of divorce will be reduced to zero.

and Allah Ta'ala Knows Best

Mufti Ebrahim Desai