Does Lanctantius Allude to Constantine's Vision?

In his work The Life of Constantine, written shortly after the great Christian Emperor’s death in 337 A.D., Eusebius of Caesarea claims that the catalyst for Constantine's conversion was a miraculous vision:

About noon, when the day was already beginning to decline, he saw with his own eyes the trophy of a cross of light in the heavens, above the sun, and bearing the inscription, CONQUER BY THIS. At this sight he was struck with amazement, and his whole army also, which followed him on this expedition, and witnessed the miracle.

Eusebius also reports that the emperor had a dream the next night in which Christ appeared to him and showed him the same sign and told him to use it as a standard in all his army’s engagements.

Some historians believe that Eusebius fabricated the account of the vision, especially since no other authors of his day-- including Constantine himself-- make mention of it. Constantine's son's tutor Lactantius made mention of the dream within a few years of the event, but omitted reference to the vision altogether. So it seems reasonable to assume that Constantine had a dream but that the tale of the vision that preceded it is an embellishment.

I think, though, that in Lactantius' account of the dream there may be a heretofore unnoticed allusion to the vision. In Of the Manner in Which the Persecutors Died, 318 Lactantius says,

Constantine was directed in a dream to cause the heavenly sign to be delineated on the shields of his soldiers, and so to proceed to battle. He did as he had been commanded, and he marked on their shields the letter X, with a perpendicular line drawn through it and turned round thus at the top, being the cipher of Christ.

It is tempting to assume that "the heavenly sign" is called "heavenly" because it is a divine or religious symbol. But what if it is called "heavenly" because the emperor had seen it in the heavens? Could this be an allusion to a prior celestial appearance?

Granted, Eusebius likely exaggerated the importance of whatever Constantine saw in the sky. A number of scholars have noticed a similarity between the vision and a solar phenomenon called the "halo effect." The most common manifestation of this phenomenon is a rainbow that forms a halo around the sun (thus its name), but others include a cross of light with the sun at its center. According to A. H. M. Jones (Constantine and the Conversion of Europe, 96), the phenomenon is caused by the fall of ice crystals across the rays of the sun. Jones says, "The display may well have been brief and unspectacular, but to Constantine’s overwrought imagination it was deeply significant."