If the main aim is to be sure to arrive on Santorini RELIAB LY in plenty of time to check in, have comfortable amount of time to orient self, stroll around, have a place for a good sundown sit, and then a dinner (elsewhere perhaps) -- then my advice from experience is -- do a flilght that goes nonstop from the Eastern US to ATH overnight. These are the only ones that reliably, day after day, month after month, land ON TIME ... anywhere from 9:15 toabout 10:30 AM depending on which airline. That's because, IF there is any delay in take-off, you have that looong flight over the Atlantic in which to make up the time. You now have more choices -- Canada Air (from Toronto) American (Philly) Delta (NYC & now Atlanta), United (Newark), also UAE from Newark I believe. With these flights, you can easily get a domestic flight on Aegean/Olympic (one airline) or Sky Express ... depending on which arrival, dep at noon or at latest, 1:30. Since u are from L.A., this does involve 3 planes, but the Europe-change option may also, with less reliability.
It's tempting to do that change in Europe, but it has its drawbacks. Sure, you can leave L.A. later & still reach your European airport by morning... but then, there may be a problem. European airports may experience traffic problems, and as others have said, the direct flights to Santorini may be on carriers like Easy Jet or Ryan, which to put it kindly, do not have the best records for equipment or on-time dep/arr. Since u only have 12 days (and is that 12 days ON the ground, or does it include flights to/from US?), you want to be prudent.
Whatever route/airline you choose for homebound trip, a final tip: Try to not book that outbound flight any earlier than 9 AM. Some are tempted by prices for 7 am deps, BUT --- You are asked to be inline at airport 2 hrs before take-off, drive to airport is 1 hr ... so it means you must leave your hotel by 4 am... so it can wreck a memorable Final Night in Athens.