Hello Jetblue! You should be in luck on the USH
-PUQ (or viceversa) route as Chile's LAN (www.lan.com) should still be operating the route. Maybe you found no options as the flight is not daily, rather, 4 x weekly.
Do you have accommodation and excursions already organised? If not, just send me a PM
and I'm sure I can be of help, as I happen to work in the industry.