Sure, you can chalk it up to interpretation. But that's not the point, the point is that the games are not intended as parodies or intentionally goofy outside of select instances. Having spoken to the developers and writers, their intentions are pretty clear to me.
What "nonsensical" aspects are you referring to? The exaggerated pseudo-science? The unintentionally poor localization or bad acting? None of these make it what you are suggesting.
GS2 CODE:Veronica is also canon.

It's a dream Claire has at the end of CV.
Yeah, a few elements were reused. The "Uroboros" enemy was one of the technical difficulties they were having with BIO4. It was difficult to model and animate due to all its individual parts and the GameCube's insufficient hardware. The origin of the Progenitor Virus is completely different, though. It has changed quite a few times with each scrapping of a new game.
Progenitor (originally known as the Clay Virus) originally didn't have anything written about how it was discovered. In the BIO4 version that became Devil May Cry, it was discovered on Mallet Island and "cultured" by the B.O.W. Nightmare from the corpses of ancient humans. The black slime surrounding that boss in DMC is actually the Progenitor Virus.
In the castle version of BIO4, the virus was discovered in the fossilized body of an ancient human (the Uroboros-like enemy and Leon's infection are also completely unrelated to the Progenitor Virus, they are something completely new). During BIO5's development, they toyed with the idea of the virus being from an aquatic plant. This changed to the dandelion-related plant in the final game.
According to Jun Takeuchi, CODE:Veronica stipulated that the virus was discovered in Africa... but I don't know if that's true. The first mention of Africa is actually in
BIO0, on the text of the file image of Marcus' Diary but not in the file text itself. It's then mentioned vaguely in
GS4.