I cleaned up the format of Louise Augusta's biography and sources so its a little easier to see what statements are supported by which sources.
This question of what we do with "common knowledge" of parentage of children is one we need to address generally in regard to the Danish royal family. Louise Augusta's own children, including her daughter Caroline Amelia, who later became the second wife and queen of Christian VIII, was generally believed to be the biological child of her mother's physician who "treated" her for infertility (by becoming her lover) after which she had 3 children following several of years of infertility with her husband. Although the research isn't done by any means, I've added some of it to the space page I created for collaborative research on the Danish royal family beginning with the Oldenborgs.
Apparently, in several such situations, potentially questionable royal lines were "cleaned up" by marrying the person of questionable parentage to someone else in the royal line. This was done with both Louise Augusta and her daughter Caroline Amelia.
I'm sure the bottom line is "include it all in the biography," but for these profiles this interconnected to the direct royal line, we need a way to create actual links between both the legal and purported biological father. Given the amount of inbreeding in these lines and the amount of time that has elapsed, it would be impossible to prove or disprove the biological connections.