Basically as it says on the tin, what if instead of renouncing Christianity Julian works on reconciling Neoplatonism and Christian philosophy/theology, in addition to his other reforms.
Now i know it wouldn't butterfly his eastern campaign completely as he needed to gain the support of the eastern legions, but purhaps without the need to prove himself to the predominantly Christian court & populace he makes a more cautious plan?
Then, instead of being Julian the Apostate, he becomes Julian the Heretic. As the example of Monothelitism will prove three centuries later, when the emperor tries to impose a compromise solution in theological areas, the only thing he is achieving is to obtain the opposition of all the contending parties against his idea. Unlike OTL, were Julian could use a
Divide et Impera to get the Christians weak by keeping them fighting each other, here he enters directly into the fray as his own particular side, fighting everyone simultaneously. Of course, he is the emperor and he can impose his will upon the Ecumenical Councils, but it will only last while he lives. Instead of getting the support of the two sides, Neoplatonism/Paganism and Christianity, he gets neither. If Julian wanted to play the Christian game (which he didn´t, because he was a true believer in Paganism, with its superstitions and mysteries, not just in neoplatonic philosophy), he needs to play it fully; that is, doing like his cousins, taking a side in the conflict between Arrianism and Orthodoxy and remain there. He can do some works on reconciliation, in the form of assimilation of Neoplatonic ideas or concepts by Christianity (it would not be the first time that pagan customs and ideas influenced it) but he must be subtle about it, and if we go by OTL, that is, he goes to Persia and dies there, he doesn´t have the time. However, if he were to have the time to do so, in the way I said, it could be doable. After all, St. Augustine of Hippo was influenced by neo-platonism. That is, it would not produce the effect or have the depth that someone like Julian would have wanted.