Before we can answer, I think a good question for you would be why you think that the HRE would necessarily need to reconcile the fact that the Romans were, at one point in their history, pagans (but, by the fall of the Western Empire, had converted officially to Christianity)

The Roman Empire was officially Christian for the last 100 years of its existence. The papacy was firmly established in Rome long before the rise of the HRE. Additionally, the Eastern Roman Emperor was seen somewhat as the temporal leader of Christianity for centuries after the fall of the West (Brownworth, Lost to the West). So I wouldn't say they necessarily saw the Romans as a pagan empire in the first place.