But that is precisely what they would be doing, getting married. The church does not consider them married until they exchange vows again. Their valid marriage begins at that point.
I’m not a canon lawyer, but I don’t think that is exactly right:
**Canon 1161.1 The retroactive validation of an invalid marriage is its validation without the renewal of consent, granted by the competent authority. It involves a dispensation from an impediment if there is one and from the canonical form if it had not been observed, as well as a referral back to the past of the canonical effects.
Canon 1161.2 The validation takes place from the moment the favour is granted; the referral back, however, is understood to have been made to the moment the marriage was celebrated, unless it is otherwise expressly provided.
Canon 1161.3 A retroactive validation is not to be granted unless it is probable that the parties intend to persevere in conjugal life.
Canon 1162.1 If consent is lacking in either or both of the parties, a marriage cannot be rectified by a retroactive validation, whether consent was absent from the beginning or, though given at the beginning, was subsequently revoked.
Canon 1162.2 If the consent was indeed absent from the beginning but was subsequently given, a retroactive validation can be granted from the moment the consent was given.
Canon 1163.1 A marriage which is invalid because of an impediment or because of defect of the legal form, can be validated retroactively, provided the consent of both parties persists.**
In other words, their process of getting married would be considered by the Church to have begun when they gave valid consent, even if their marriage originally lacked canonical form. It is my understanding that in a case such as the OP’s, once the marriage is convalidated the couple can rightly say, “We have been married since _______” and give their original civil wedding date. It is only if their original consent was defective (which it might have been; this is another issue) that they would be starting from scratch, so to speak.