"Masculinity" means possesion of masculine traits or appearance, while "butchiosity" introduces a note of irony: the appearance or trying to act in a conventionally or socially-acceptable masculine manner expected by the straight world.
"Butchness" is problematic, as it is not consisently used to mean the quality of visible masculinity; instead, the user is often forced into grammatical adaptations like "He behaves in a butch way," or "Sometimes he overcompensates and out-butches himself."
"Butchiosity" is almost certainly a back-formation inspired by the 1977 Woody Allen movie ANNIE HALL (screen play: W. Allen and Marshall Brickman): "Was it heavy a rock concert? Did it achieve . . . heaviosity?"
"Who is that great-looking hunk?" "Oh, him satirically, "her". He looks like a tower of butchiosity but on the inside there's a major flaming queen screaming to be let out."
Compared to "masculinity," "butchiosity" introduces a note of irony: the appearance of masculinity, or trying to appear conventionally masculine. Machismo is lexically coherent as a loan-word from Spanish but has connotations of an ingrained, often unacceptable and patriarchal behavior, overmasculine from the start; or old-fashioned notions of being a man. Instead, "butchiosity"comes with a twist: it can imply a trying-too-hard, self-conscious or overstudied presentation of an image of masculinity, especially in an attempt to meet the straight world's expectations of same.
An act not a trait, as it were.