Man sorry about the timing on the AA award.

I wouldn't do a RTW, unless you have many more destinations in mind.

For the Asia portion, I would consider using your AA miles or your SPG to a variety of programs. AA has off-peak awards in Asia until the end of this month, and Oneworld has a good footprint in Asia. But I'm not as familiar with those and maybe someone else will be able to judge if you can use that to your advantage. But you could also use SPG to BA and JAL, which have distance based ideas, like the AA award that vanished. Be aware of taxes and fees though. Especially for your Asian travels I would look at AA or BA redemptions using CX. Also Alaska has good CX redemptions, you could consider that for the Asia and SE Asia flights.

For getting around in SE Asia, you might just buy some of those. Consider your personal value, and if saving the cash is better for you even if the redemption isn't a great cost per mile. There are several budget carriers that have very good prices at times in this area.