Hi everyone,
Wanted to check back in to follow up on this thread as I am now in the US with my dog (yey!) who is safe and happy as can be. Las Lunas was great: http://www.latampettransport.com/destinations/argentina/
Responsive, friendly, genuinely care about your pet. After picking my dog up, they sent me photos and videos of him throughout the day (leading up to his check in), including one where they were feeding him his medicine. Totally recommend them.
As a side note - I flew United and used their "pet safe program" I was advised to choose a longer layover in Houston (en route to NJ) so that they could take him out of his crate, walk and feed him and deal with customs procedures. The United customer service rep suggested a 3-4 hour layover. Well - when he arrived in NJ it didn't look as if he had been taken out for that break - the food that Las Lunas had provided was still in a bag taped to the outside of the crate and he didn't look like a dog who had been let out 4 hours prior. He peed a lake on the airport floor because the poor guy had been holding it for god knows how long. I'm so thankful that he arrived safely in the end but kicking myself for making him do that long layover when I had a way shorter layover option.