hirhur k'dibbur by kiddush and more on the topic of arvus

The Tur (O.C. 273) quotes an opinion of the Geonim that one who has already said kiddush may not recite kiddush for someone else, with the caveat according to the BH”G that the other people know how to say kiddush. The Tur disagrees based on the principle of arvus which tells us “yatzah – motzi”, even someone who already fulfilled a mitzvah can be motzi someone who has not. The Sha’agas Arye (#13) explains that this dispute is l’shitasam of the dispute Tosfos and BH”G discussed yesterday. According to BH”G, one who ate a k’zayis (whose chiyuv in bentching is derabbanan) cannot be motzi someone who ate k’dei seviya (whose chiyuv is d’oraysa) in bentching because arvus does not work on a chiyuv bracha d’oraysa, only on chiyuvim derabbanan. Tosfos disagrees. The S.A. argues that since kiddush is a bracha d’oraysa, the opinions line up - the Geonim and BH”G do not extend arvus to brachos d’oraysa, and the Tur following the view of Tosfos that arvus applies across the board. (I am unclear on how the Sha’agas Arye explains the BH”G’s distinction between the case of listeners who know how to say kiddush and those who don’t – arvus according to BH”G and Geonim should be categorically excluded.) The Sha'agas Arye proves from this machlokes that we do not apply the principle of “hirhur k’dibbur” to kiddush - the words of kiddush must be articulated, and merely thinking about kedushas shabbos does not fulfill the mitzvah of “zachor es yom haShabbos”. If one could be yotzei kiddush through hirhur, then reciting the bracha would only be a kiyum derabbanan, and the principle of arvus should apply according to all.
In light of the Pri Megadim that we started this whole discussion with, is this proof of the Sha'agas Arye convincing? If one does not get a kiyum d’oraysa for a mitzvah unless done in the format which the Chachamim specified (the PM"G's chiddush), or as Chaim Markowitz put it, dinim derabbanan are extensions of the din d’oraysa and become an inherent part of their kiyum, then how do we know that the Geonim and Tur assume reciting kiddush is a d’oraysa because one does not apply “hirhur k’dibbur”? Maybe m’doraysa we do say “hirhur k’dibbur”, but once the Chachamim instituted a specific nussach habracha, one does not gain a kiyum mitzvah d’oraysa unless the format and nussach specified by the Chachamim is followed?!