Ultimately, we ended up staying at the airport and getting a lot of reading done in the food court area while eating Chifa. Originally, we had planned on buying lounge passes for Sumaq, but we were unable to get our boarding passes until 3 hours before the flight as the AA desk did not open until then and we were unable to check in online due to a slight mismatch between the name on our ticket and passport (hyphenated name problems). By that point, it didn't really seem worth it.