Much earlier this year I did a post (part I, II, III) on the unusual circumstance of someone who comes to shul very late on Shmini Atzeres, when the tzibur is up to musaf, and he/she hears mashiv ha'ruach announced before he/she has davened shacharis -- should he/she (this happened to my daughter) say mashiv ha'ruach in their tefilas shacharis, or wait until musaf like everyone else? No special reason to post on it again now except for the fact that I finally found someone who deals with this issue. Had I been more familiar with the history of my current home town I might have known the answer back then.
Back in the early days of Cedarhurst, NY (before my time), one of the Rabbonim who settled in the community was R' Nachum Tzvi Kornmehl. Rav Kornmehl had been a rav in Vienna before the war and then upstate NY in Albany and Rochester, and from what I understand he came to Cedarhurst thinking of retirement, not of the next move in a long career of rabbanus. Hashem had his own plans and Rav Kornmehl ended up leading the Young Israel of Cedarhurst, which then stood in a building about the size of a large house (I think Rav Kornmehl lived there as well), about a fifth of the size of its current edifice. In his Shu"T Tiferes Tzvi (II:39 - available here) he opines that in the case I described mashiv ha'ruach should not be said in shacharis. Aside from the logic of not creating two different minhagim with respect to shacharis, he also makes a textual diyuk. The Mishna, in discussing the recitation of mashiv ha'ruach, writes that "Ha'acharon [the one who davens musaf] mazkir v'harishom [the one who davens shacharis] aino mazkir." Since shacharis comes first, shouldn't the Mishna first tell us that the rishon does not say mashiv ha'ruach and then tell us that the acharon, the one davening musaf, does? And why use the terms rishon and acharon instead of shacharis and musaf? Rav Kornmehl suggests that the Mishna is discussing our very case -- the tzibur is already prepared for musaf, yet there is still a straggler who has not davened shacharis. The tzibur will be saying mashiv ha'ruch, but the rishon who has not yet davened shacharis (it's not shacharis time anymore for the tzibur, so the Mishna does not refer to it as such) will not.
I don't know if the diyuk alone is enough to convince you, but its sharp.