Thanks for your post- I'm looking at similar itineraries. (Easter island/machu pichu & Tahiti). I have 112k British Airways Avios & 300k AA miles, along with Hilton & 2 sign up bonuses for Intercontinental (which will= 4 nights in bora bora).

You can use expertflyer to see availability for AA on Air tahiti nui (you then have to call AA to book it). Search LAX- PPT online. We are flying from ORD. I can't remember if expertflyer allowed you to search ORD- PPT, or if I had to do ORD-LAX, LAX-PPT? Anyway, when I called to put it on hold, it was 37.5/62.5 as you mentioned above.

One other thing I noticed: Depending on day/flight times, you can avoid doing that night in Tahiti if you choose a date/time that has you arriving into PPT early am (5am ish). Our plan was to take one of those flights, then hop onto the flight to Bora bora. Would also be interested in any tips/advice