Pretty interesting stuff in the main, though, like Penguin I'd like more information.
One big problem these researchers run into initially is the timing. I still hear from time to time the story of Constantine's dramatic conversion at the Milvian Bridge, but the chronicles don't bear it out. Most contemporary histories agree that the emperor didn't convert until he lay on his death bed, some 18-19 years later. This seems more in line with the behavior of other Roman rulers that had to deal with Christianity. Those that weren't outright hostile and into the whole lion/Christian Caesar salad were quite prone to deathbed conversions. They were Romans, after all, and Rome was never too keen on throwing out gods, any of them, because they might turn out to be useful. Its quite possible, then, that Constantine, like many before and after him, was just covering his bases.