Answer

Happy holidays.
It is explained there in the Talmud that the doubt is about what that person intended. Let me preface this with a principle: wherever the Talmud is uncertain about a person’s intent, there is no reason to treat the Talmud as binding precedent. One must examine the language in the place and time being discussed, and on that basis decide what the person meant. If the Talmud determines that “designated” means “betrothed,” but today no one uses language like that at all, would we still rule that way because the Talmud ruled that way? This is a factual question of what the person meant, and that must be decided by looking at the situation before you, not by looking in the Talmud. This is a paradigm for many topics that are completely irrelevant today, and the commentators and halakhic decisors get tangled up in them for no reason, but I won’t go into that here.
As for our case, “engaged in that matter” means engaged in betrothal according to the law of Moses and Israel. If the couple is not marrying according to the law of Moses and Israel and does not intend that, then the groom’s intent in his statements is irrelevant. I understand that you are speaking about a couple marrying according to the law of Moses and Israel, except that the groom changed the accepted wording. You have to assess exactly what he means, and decide accordingly.
Incidentally, “engaged in that matter” also appears, at least on the face of it, to be only an indication for the factual presumption regarding his intent, and therefore here too the Talmud’s determinations are not really relevant. However, here there may perhaps be room to distinguish, because in the accepted conception of betrothal, the statement has a constitutive halakhic status. It does not come only to clarify his intention; it is also a condition for the betrothal to take effect. According to that, the rule of “engaged in that matter” is not merely a clarification of his intention, but turns the statement into a betrothal statement and thereby validates the betrothal itself. If so, there is a halakhic novelty in the rule of “engaged in that matter,” and this is not merely an evaluation of intention.
Still, for the case at hand, it is clear that such a couple is entirely engaged in that matter, and therefore if we decide that his wording means betrothal, there will be no formal problem of requiring a statement, because being engaged in that matter causes the statement to be considered a valid betrothal statement. What remains is only the question of intention, and that must be determined according to the assessment of the rabbi on site. But if there is doubt about the wording, then the question whether they are very much engaged in that matter or somewhat less engaged in that matter is irrelevant. Therefore I do not agree with the a fortiori argument you made from the “engaged in that matter” discussed in the Talmud. Even if in your case they are fully engaged in that matter, one still has to decide what he means by his wording. And if the wording is doubtful, then even if they are fully engaged in that matter, that should not make a difference, and we still have a doubtful betrothal00a0(unless in your view, because of the context, the intention is no longer doubtful; but that could also be true in the Talmud’s case of being engaged in that matter).