This logline is getting better, now to cut the word count and get specific.
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1) Demonic and dark is redundant, use one or the other (or just use the word demon)
2) Spunky yet Meticulous: A spunky person flies by the seat of their pants, they go-for-it, a meticulous person doesn't; I would keep spunky and drop meticulous
3) Misjudges his technical abilities: This isn't needed, drop it
4) ---and unknowingly: Drop this, if he doesn't know it, how does he know to go back in time and change it.
5) Makes the devastation worse: Be specific, this is the crux of the logline. How does he make the devastation worse? ?Does he open a portal to hell? Does he accidentally set the auto-pilot to crash the plane into a mountain? Tell us how he makes the devastation worse. This is the inciting incident and very important to the logline.
6) Consequently: Drop this
7) Using an enchanted relic: Be specific.?What relic? You should watch Buffy the Vampire slayer, every relic had a name, every relic had a history--- Orb of Thesulah, gem of amara--- you should tell us what relic sends him back in time, give it a name.
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"When his flight is attacked by demons, a spunky Greek curator accidentally opens a doorway to hell and must use the gem of Chronos to travel back in time to undo the damage and stop the dark-ones from taking over the world."
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Hope that helped, good luck with this!