Great TR. We did a similar trip to Machu Pichu in 2010 from IAH to Lima (on Continental) and then to Cusco by TACA. Returned via Panama city by COPA and then by Continental. IAH-Lima-PTY-IAH by award travel (35,000 miles is a great bargain for this long route).
LAN Peru is expensive from Lima to Cusco, and TACA is a good alternative, but all Peruvian citizens and residents get a big discount on the local travel, which is not available to foreigners.