Waiting between meat and milk, the Yekke 3 hour minhag, and what do you do when minhag avotainu is based on a mistake

Rav Asi asked Rabbi Yochanan How long should one wait between [eating] meat and cheese? He said, "Not at all." Really? But Rav Chisda said, One who eats meat isn't allowed to eat cheese, [one who eats] cheese is allowed to eat meat. Rather [Rav Asi must have asked] How long should one wait between [eating] cheese and meat? He said, "Not at all."

...

Mar Ukva says, In comparison to my father, regarding this matter, I am vinegar the son of wine. My father, when he ate meat, would not eat cheese until the same time the next day. But I, even if I won't eat it at this meal, I'll eat it at the next meal.

"At the next meal I'll eat": Not just at the meal that is customary - one in the morning and one in the evening - rather even immediately, if you clear the table and make the concluding blessing, it's permissible, since the Rabbi's didn't differentiate.

The Behag (9th century) writes that one who eats meat can eat dairy immediately afterwards as long as there is wiping and washing of the hands.

(28) One who eats meat first, whether domesticated animal or fowl, does not eat milk afterwards until he waits between them the measure of time until another meal, and that is about six hours, because of the meat between his teeth that is not removed with wiping.

And my father the Rosh (1259-1327) writes that this is not the minhag, rather after eating meat one cannot eat dairy, even if it was fowl, and do not change this minhag to wait an amount of time equal to the time between the morning meal and the evening meal between meat and dairy.

(1) One who eats meat, even of a wild animal or fowl, does not eat cheese afterwards until he waits six hours.

There are those that says that he doesn't have to wait six hours, but rather immediately if he finishes the meal and says the concluding blessing, it is permissible after wiping and rinsing his mouth (Tosafot Hullin 105a - "At the next meal", Mordechai chapter 25, Haga'ot Ashiri, Haga'ot Maimoniot chapter 9 of forbidden foods, and Ravya). The simple custom in our countries is to wait after eating meat one hour and to eat cheese afterwards, but you have to say the concluding blessing after the meat (HaAruch, Haga'ot Shaarei Dura) because then it's like a new meal and permissible to eat according to the lenient view. But with no blessing, waiting alone does not good.

[If] one ate meat, it is forbidden to eat cheese until [waiting for] another meal. This follows the opinion of Rav Chisda (Perek Kol Habasar, Chullin 105a). This is also the opinion of Mar Ukva since the meat and fat stay in one's mouth a long time, as well as Rabeinu Baruch who says that the meat between the teeth is called meat, as it says: "the meat was still between their teeth" (Bamidbar 11:33). The time is three hours, per Rashi. For this reason it is good to pick one's teeth after the meal if one will be eating cheese.

Do not nullify any minhag or ridicule it, for it was not enacted in vain.

...I say minhag yisrael is a commandment

Sometimes, minhag is genenom. [Note that minhag spelled backwards is gehenom - something first cited in Shiltei Giborim in the name of Rabeinu Tam].