Between your BKK trip and your trip to Germany, you'd easily clear the challenge.
It's even possible to clear the challenge with just the LAX-BKK trip, if you can finagle the correct routing out of AA.
If you flew LAX-DFW-NRT-BKK return, that's 10,545 miles each way, which would put you over the top. LAX-ORD-NRT-BKK is 10,900 miles each way, which would also put you over the top. The bad news is that LAX/BKK on AA is a MPM fare, and the Pacifc Routing MPM (which is what you need for the cheap fares) is only 9,898.
If you're friends with an AA CTO agent, then you could probably book yourself on LAX-NRT-BKK using the JL code-shares, and have the CTO agent pop you over to connections in DFW or ORD, even though it exceeds the MPM.
As an alternative, if you want to earn Status on AA in a fun way, while you're in BKK, fly BKK-SDY return on BA or QF. The fare is under $1700 in Biz, and only around $2,000 in FC. It's 4676 miles each way, so one round trip in Biz or FC will complete the challenge. And you get to fly premium on a really nice airline...