[alternatives?]

“I’d guess that it peaked between 1200 and 1347.”

I had to look up why you selected 1347. Seemed Spock like. That is when the Bubonic Plague reached Europe. Very impressive.

[alexander_busek]

"Constantinople; summer, 1334. It marched through the streets, the sewers. It left the city by oxcart, by sea, to kill half of Europe. The rats, rustling and squealing in the night as they, too, died. The rats..."

Regards from a "student of history"

[alternatives?]

I typed “Germany 1347” in Bing and obtained the same information.

[Hieronymus]

1200 is at the beginning of the rise of the Mendicant Orders (primarily the Franciscans and the Dominicans) which marks a diversifying of options for the religiously inclined. This increase in diversity coupled with the drop in population a century and a half later favours the earlier part of the window, but pretty well ensures that at no point after the window do the numbers reach those of the glory days.