I just did CUZ-LIM-JFK this weekend, and recommend that you allow for a large margin of error with your CUZ-LIM flight. Even if you arrive on time, you will likely need to check in again, go through security and then immigration. It took me a bit over an hour, although that was in the evening when there were lots of international flights.

Also, the CUZ-LIM are cancelled/delayed very often. The weather looked fine to me, yet my first flight was cancelled so I was moved to one an hour later, then that flight was delayed an hour. From what I understand that is very common. If you do do the same day CUZ-LIM, choose one of the first flights of the day so that you can roll back several flights if need be and still make your connection.