I spent some time investigating the three hour yekke minhag, and Prof. Sperber told me he thought my theory is reasonable.
I’ll make it short.
The position that the minhag comes from Rabeinu Yerucham is far fetched, and in my opinion, untenable. As is known, he specifically says six hours in another sefer of his. Two, it’s very likely that the letter gimel was a ta’us sofer, it’s only one letter. Three, and more important, Rabeinu Yerucham was French, a talmid of Rabeinu Peretz of Corbeil (south of Paris), and until proven otherwise, had zero influence on German custom. He could not possibly have taken an entrenched German custom and single-handedly, without talmudic proof, changed it to three hours, and that only in Germany and not in France or C’na’an.. No way. Four, no one else mentions it.
The minhag is only several hundred years old, as witnessed by the Mizmor L’david’s dealing with it, a first in rabbinic literature. To base it on the Pri Chadash is interesting, but irrelevant, the Italian Chezkiyah de Silva had no authority or influence in Germany.
In the 1700s ,the eating patterns of the Germans , Jews and non-Jews alike changed, and with it, meal times. This has been documented. The evening dairy meal gradually moved earlier so that it would be served in the daytime. Considering that the winter days are short, if earlier in the day there was a meat meal, which certainly occurred on shabbat and yom tov, there were only approximately three-four hours left in the day. Hence, by sociological neccessity, and without changing the halachah (Ashkenaz psak according to the ba’alei hatosfot was not to wait at all,so it’s a minor change mid’rabanan to cut from six to three), the wait was cut to three.
This theory answers several important questions, namely:
1. Where is the source for three hours in the rishonim? There is none, nor was one necessary.
2. Why was it never mentioned until the 1700s? It didn’t exist yet.
3. Why only in Germany? That’s where eating patterns changed.
I have no definitive proof. It is a theory, even conjecture if you desire. You can knock it down, be my guest. But it makes more sense to me than anything else I’ve heard.