I'm not a "Skyper" (I've used whatsapp and viber occasionally though). Don't they have to be a "contact"?

So the way I solved my problem was I called the AMEX Platinum concierge desk. After a bit of confusion (they really wanted to try to book the reservation on their CRS), they found an agent who spoke Spanish who called down to Sky and patched me in. The agent spoke good English, and was able to pull up my failed online reservation with my passport number (a bit weird, but good). I gave them payment over the phone, at the same price as on the website.

I asked the agent why this transaction failed (I tried several USA credit cards) when my previous order worked, and she said sometimes int'l cards work, and sometimes they don't. Logically, if I'm running an airline, I'd want to sell as many tickets as I could so I'd try to fix this payment problem, but Sky may have other priorities.

BTW, LATAM wasn't anywhere near Sky price-wise for this trip. I don't know whether that's random, or whether LATAM has now decided that they need to be less price-competitive. Honestly, I don't think most Chileans would pay a lot more to fly LATAM.