Although I'm not religious I'm a sucker for Church history. This has always stood out to me as one of those 'querks' which is never fully accounted for by contempories of the time. I have dabbled in Barnes' book 'Constantine: Dynasty, Religion and Power in the Later Roman Empire', where Barnes seems to argue that Constantine's affiliation with Paganism is simply out of respect for his Pagan subjects, but I'm left wondering what other academics make of this. Any pointers towards books, articles, etc would be much appreciated!
This is a very complex question that has no settled answer as far as I am aware. Barnes makes the case that Constantine was somewhat of an evangelist after his conversion: Constantinople as an overtly Christian city, the banning of sacrifice in territories liberated from Licinius, favorable treatment for Christian municipalities, etc.. He even suggests that Constantine's mother may have been a Christian based on the name of one of his sisters.
Most other scholars acknowledge Constantine's conversion as genuine, but disagree on how far Constantine went in portraying himself as an exclusively Christian ruler. For instance, we have evidence that there was a massive statue of Constantine in the guise of Sol Invictus erected in Constantinople which would cast doubt on his intention to found a Christian capital.
Another problem with assessing the 'Christianess' of Constantine is the gap between our modern view of Christianity and the Christianity (or more accurately Christianities) that existed in his time. The church of the fourth century was a loosely associated grouping of largely independent bishoprics that each had its own traditions and doctrinal interpretations. Most of them were not as hostile to existing traditions as modern people believe them to be. Constantine has become a victim of his own success in this regard as one of the main innovations he introduced to the church was the idea of a universal orthodoxy that could be enforced with the coercive power of the state. This orthodoxy has shifted over time to such an extent that it has called Constantine's own belief into question.
There may in fact be no contradiction to reconcile. Constantine identified as a Christian after his defeat of Maxentius, but the vocabulary for communicating this to his subjects had not yet been developed so he borrowed from existing archetypes they would understand. He may have needed to use these archetypes himself to understand his newly adopted faith because at the time there was no clearly defined universal idea of what it was to be a christian.