Is it permissible to re-formulate the marriage contract verbally in the presence of the guardian and witnesses so that it becomes Islamically valid and free of doubt, knowing that the first contract was concluded without a guardian, based on the fatwa of two marriage officials in the questioner's country?

The matter is as you mentioned, regarding the difference of opinion between the majority of scholars (jumhur (definition)) and the Hanafis concerning the ruling on marriage without a guardian (wali). The jumhur hold it to be invalid, while Abu Hanifa holds it to be valid. Since your marriage was conducted in imitation of Abu Hanifa and according to what is practiced in the country, it is valid, and there is no need to renew the contract. It is stated in "Matalib Uli al-Nuha" by Al-Ruhaibani Al-Hanbali that a Hanbali judge is not permitted to punish someone who imitates Abu Hanifa in contracting a marriage without a guardian, due to the absence of disobedience. And if a Hanafi judge rules it to be valid, and then the matter is referred to a Hanbali judge, the latter must enforce it. Based on this, your marriage is valid, and there is no need to renew the contract.