Apparently, contrōversus comes from the preposition contrā- + versus. So why does it have "ō" instead of "ā"? I checked Lewis and Short, but it doesn't explain the development of this vowel. I also found that contrāversus does in fact exist, although it seems to have a different meaning.
Just as we have both intrā and intrō, citrā/citrō, ultrā/ultrō, there used to be a form contrō, which has only survived in this word. De Vaan adduces an Oscan form contrud. Historically, the -ō forms are masc./neut. ablatives, the -ā forms are fem. ablatives.