Advice noted if I ever get to South America!
Thanks for the tips everyone else - I decided to fly into PEN on CX. I will lose two hours in PEN but at least I am saved from the hassles in Singapore and Jetstar Asia.
For those flying in Asia, I highly recommend booking J class fares on CX out of TPE as a SC run. I am able to fly CX in J for only around $150 more across all my flights than JQ in Y as I will have luggage etc.....money well spent I think!