Historians widely agree that Justinian did indeed issue an edict imposing aphthartodocetism (the idea that Jesus's body was always incorruptible), citing the testimony you quoted from Evagrius Scholasticus.

One of the primary theological issues that Justinian faced was related to the nature of the incarnation of Jesus – advocates of the Chalcedonian Definition on one side, and those supporting Monophysitism (or, more charitably, Miaphysitism) on the other. Justinian made various efforts to achieve unity during his rule (cf. the Three-Chapter Controversy), and it seems that near the end of his life, he thought that one way to achieve that might be by imposing aphthartodocetism. Adolf von Harnack writes:

[Justinian] could not find the right dogmatic formula for the World-Empire which he created; what he did settle was the specific formula for the patriarchate of Constantinople and its immediate belongings. He, however, saw that himself; he wished to sanction Aphthartodoketism (564) which was in harmony with his own dogmatic views and which might perhaps win over the Monophysites. His policy was a logical one, and the Emperor set about carrying it out with his wonted energy, beginning as usual by deposing the patriarch of the capital. (History of Dogma, IV, 251)

Similarly, J. A. S. Evans attributes political motives to Justinian on this matter, and traces several efforts to resolve the controversy leading up to the edict:

[Bishop Theodore Askidas] reminded the old emperor that there was more than one Monophysite sect, and if he could not win over the followers of Severus, why not approach the Aphthartodocetists? The suggestion must have piqued the emperor's interest. In 557, he had convoked Jacob Baradaeus and a large selection of his monks in Constantinople in another effort to solve the Monophysite problem, but the meeting had been fruitless. On the eve of the rededication of Hagia Sophia, he issued an edict proclaiming the orthodoxy of Chalcedon. But then, near the end of 564, he promulgated an edict affirming the incorruptibility of Christ's body. (Age of Justinian, 262)

Other historians more readily attribute this change to a mental decline; J. B. Bury, History of the Later Roman Empire, II (393), indicates that it "is generally considered an aberration due to senility." Others hold that the change was compatible with his long-held beliefs:

[Justinian's] edict on the incorruptibility of Christ's body (564 or 565) is difficult to understand. Even though the emperor's aphthartodocetic views most likely had a place within his Chalcedonian convictions, they show once again how until his very last breath he attempted to describe the union of the natures in Christ in a language that would be acceptable to (a major segment of) the anti-Chalcedonians. (Lucas Van Rompay, in Cambridge Companion to the Age of Justinian, 254)

Even the Catholic Encyclopedia, though calling him a "wonderful" and "great" man, is largely negative regarding his ecclesiastical polity. The aphthartodocetism edict is not explicitly mentioned, but his various interventions in the Monophysite controversies earn him the labels "semi-Monophysite" and "a persecutor of the Church."

Despite all this agreement, there is at least one prominent dissenter, Asterios Gerostergios, an Eastern Orthodox thinker. He defends Justinian's reputation, casting doubt on the reliability of Evagrius and arguing that such a significant edict would have been mentioned in a variety of other contexts if it actually existed. For details, see this summary, or Gerostergios's book, Justinian the Great.

Summary

The argument from silence of Asterios Gerostergios does seem to have some merit, and as in many questions of early medieval history, we might desire that more evidence survived. Nonetheless, while recognizing that absolute certainty is impossible, it is difficult to reject the consensus view – that Justinian did indeed issue an edict imposing aphthartodocetism. What his mental condition and motives were at the time, however, is less certain.

As for the possibility of a deathbed rejection of aphthartodocetism, we lack evidence of events immediately surrounding his death. But all indications suggest that Justinian pursued the enforcement of his edict until his death.