Obviusly you want to book as many legs as possible as AA codeshares to increase your AAdvantage earnings. You also have 2 more sectors available, so could fly JFK-SJU-LAX-LIM for example. But L is not a good way to earn status, which is the point of the challenge, so probably you are on the right track and better off to earn it with flights ahead of your LONE5 trip. Also you need to get the physical Platinum card for lounge access in many of your destinations, which might be hard to do once you are travelling.