Just to follow up, I never found anyone from COPA in Santiago who could help me out. I finally gave up and just went across the street to the Holiday Inn and booked a room for the night on my own dime. I got through to the LAN helpline as I was boarding in Houston and was able to officially change my reservation for the LAN flight to the time I wanted the following day, though I had to pay a difference of fare ($35) since they only had Y class available. It also did something else weird to my reservation (changed my passport number), so I still had to find one of the many LAN desks in Santiago and ask them to sort it out. Only took a few minutes, though.

Also, my bag didn't make it on to La Serena. As far as I know, it's still stuck in Santiago and won't arrive until tomorrow. Not the least bit surprising, given the combination of irrops and passing through the hands of 3 different airlines...