Checkliste vs. Prüfliste
mh, "und" is very uncommon as a translation for checklist ... "Checkliste" is very common and it is the word mainly used in german for lists of points to check. I proved it with many sources. There is no need you search for sources cause i did. But there is no need to ignore so many sources either.
About theory i don't know much, but i doubt your explanation because it is a compound already in english and is adopted completely (in the sense of "eingedeutscht") in german long before we were born. It is a german word now like "Basketball" with complete declinations (Duden). (see, Basketball is a compound in english, as well, and is adopted as such complete. The idea is funny, thinking Basketball was split once in two words and the english word "basket" was compound then with the german word Ball ... no.)