You might only be able to upgrade the BA flights if any at all. I don't know if you need a J fare or if a D one is eligible. However, since you only joined BA, you probably will not have enough miles even when your last BA segment comes along.

If it's miles that you are after, I highly recommend enrolling for a Gold and Platinum challenge with AA (search in that forum).

You could also fit in more sectors within Asia and South America if time is not an issue.