Tried looking at the airlines that serve JTR?
https://en.m.wikipedia.org/wiki/Sant...tional_Airport
Your AS mileage choices are BA and DE. No AA/AF/EK/KL. Are you looking for July 2017 or July 2018? Might note you are picking prime time for Europeans to vacation someplace like JTR, so DE (which specializes in European vacation flying) might not be offering a lot of inventory... and for 2017 the redemption inventory might be gone.
I would likely buy cheap LCC tickets and make a multi-stop trip of it.