I recommend taking the following shortest path which I timed for the flights on March 8th;
1) LATAM flight from LPB 10.15am to LIMA 11.15am; Then LATAM flight again from LIMA12.20pm to LAX 6pm; (11.45 minutes total travel time)
2) Then AA nonstop 3hrs from LAX 7.56pm to YVR 11.10pm. (under 17 hour total travel time)
Cost for the 1st segment is $871 and the 2nd segment is $472.
Award booking for LATAM is easy to do with 30,000 AA miles by calling AAdvantage number (not bookable online); You can easily get 50,000 AA miles by opening Barclay AA Aviator card without any minimum purchase spend requirement.