Who wrote Psalms 22?

Many Christian traditions argue Psalm 22 was written by King David (circa 1000 BCE). It is often viewed as a prophetic lament foreshadowing Jesus' crucifixion. In exegetical scholarship, however, Psalm 22 is widely treated as a composite composition. Chronologically the core material is dated to the pre-exilic period (that is, before the Babylonian destruction of Jerusalem in 587 BCE). The appended thanksgiving that celebrates Israel’s rescue is therefore usually regarded as a post-exilic accretion. The final stratum, science tells us, is written during the Hellenistic period (late fourth century BCE). It is a bit uncertain when king David lived, but historians place his life between 10th century BCE and 9th century BCE. If Psalm 22 was written 500 years after King David, he cannot have anything to do with it. Scientific analysis also reveals that it most likely has multiple origins. So how can the 500 years discrepancy between what science and historians tell us, and what most Christian tradition teach regarding attribution?