This is not meant to be a definitive answer, and is based on dialect as opposed to proper English grammar--more of a commentary than an answer per se.
In colloquial American English, "completely Oxford" would be easily understood in the sense of "totally Oxford". ("Totally" has been a popular term in colloquial American English.) Thus is works, but perhaps not in the context in which you intend to use it, where more words are necessary to convey the precise meaning.
- "Absolutely Oxford" is superior because of the alliterative quality
It has a better ring, but is not otherwise distinct structurally, so far as I know, in that completely and absolutely are both adverbs and synonyms.