Answer (part I): [We sent the new mother our previous response,[1] in which we posited that a woman can recite HaGomel up to twelve months from the time of the birth.]

Question (part II): Before I sent you the question, I followed a ruling that I found online that if one is not sure whether he needs to recite HaGomel, he should have in mind during the morning beracha of “hagomel chasadim tovim l’amo Yisrael [Who grants good acts of kindness to His nation Israel]” that it should also serve as thanks in lieu of Birkat HaGomel. After having done that, can I still follow your ruling and recite the regular HaGomel, or would that now be a beracha l’vatala?

Answer (part II): The advice you found on the internet has complicated matters – not because it is illegitimate, but specifically because it has a significant basis.
The Shulchan Aruch[2] suggests that in the event that it is not clear whether one fulfilled the mitzva of making Birkat HaGomel, it is advisable to recite the content of the beracha without HaShem’s Name. The idea you saw – having intention during the morning beracha that resembles HaGomel’s language to also fulfill a requirement of Birkat HaGomel that is subject to doubt – seems to come from Halichot Shlomo,[3] citing R. Shlomo Zalman Auerbach, which claims that it is a better alternative to the Shulchan Aruch’s idea. The two berachot indeed share the word “hagomel” (Who grants) and the root “tov” (goodness). There are differences between them, however, and only HaGomel is in full beracha form (including “Elokeinu Melech ha’olam”). For support, Halichot Shlomo points out that the text of HaGomel, as found in the gemara[4] and accepted by several Rishonim, is precisely “gomel chasadim tovim.” Although the Beit Yosef accepts the view of the Rishonim who use our present text, “hagomel l’chayavim tovot,” the other text is presumably valid at least b’di’eved. (There is flexibility in the language of Birkat HaGomel.[5]) Therefore, according to Halichot Shlomo, you have already fulfilled the mitzva, and if you were to recite the standard text at this point, it would be a beracha l’vatala.
Indeed, there is apparent great gain in the Halichot Shlomo’s suggestion, as a valid beracha must include HaShem’s name,[6] which the Shulchan Aruch’s suggestion omits. We know of two possible rationales for the Shulchan Aruch’s view: 1) According to a minority opinion, one fulfills the beracha in this form;[7] 2) A non-beracha declaration in order to thank HaShem has value, even if it does not fulfill the formal beracha obligation.[8]
On the other hand, there are questions about the value of what you did in following the Halichot Shlomo’s idea. First, while it is possible, it is difficult for an authority, even of Rav Auerbach’s great stature, to argue against the Shulchan Aruch and present an idea that is not directly based on a classical source.[9] Furthermore, the proposition that the two berachot are similar is far from obvious. Note that HaGomel gives thanks for a personal salvation, as it concludes with words “shegemalani kol tov,”[10] whereas the morning beracha mentions general “good acts of kindness to His nation Israel” but does not stress the welfare of the blesser. In fact, it is possible that the Birkat HaGomel text found in the gemara assumes that one would conclude with “shegemalani kol tov.”[11] Halichot Shlomo[12] suggests adding the phrase “shegemalani kol tov” to the end of the morning beracha, which could improve matters, but it does not sound like you did this (you would remember, as it would have entailed concentration). Moreover, you imply that you said the beracha normally, i.e., to yourself, and one is supposed to recite HaGomel in a manner that ten people can hear.[13] The Shulchan Aruch[14] cites two opinions as to whether one fulfilled his obligation b’di’eved if he did not do it in front of ten. Due to one or all of these reasons, it is possible that you did not fulfill Birkat HaGomel.
Despite our doubts about your implementation of Rav Auerbach’s idea, we would not tell you to make another beracha. According to almost all poskim, the rule that one does not make berachot in cases of doubt applies to HaGomel.[15] Although you are not required to do anything further, the possibility of using the Shulchan Aruch’s approach of publicly reciting HaGomel without HaShem’s Name certainly exists. However, considering that you need not rush, there is a seemingly better and more convenient option for you, which is fully accepted and is also found in the Shulchan Aruch.[16] Have someone else who needs to recite HaGomel have in mind for the beracha to apply to the two of you as she recites it, while you are present and intending the same.