Is it permissible to pay zakat to a recent convert Muslim wife on the basis of her being "whose hearts are to be reconciled," and for how long can she be considered as such?

It is not permissible to give zakat to one's wife on the basis that she is among those whose hearts are to be reconciled (al-mu'allafati qulubuhum), for not everyone who embraces Islam is considered to be among them. The Muslim category of "those whose hearts are to be reconciled" comprises four types: influential leaders who have embraced Islam but whose intentions are weak, so they are given [zakat] to strengthen their faith; people of status who have embraced Islam and are given [zakat] to encourage their counterparts among the disbelievers to embrace Islam; a group given [zakat] to fight against the disbelievers adjacent to them and protect the Muslims adjacent to them; and a group given [zakat] to collect zakat from those who withhold it. Your wife does not fall into any of these categories.