Rather than searching for a roundtrip redemption from a single FFP, I would look at separate one-way redemptions. Chase has some different airline transfer partners than Amex does. Unfortunately, neither transfers to AA, which has a 60,000-mile Business Class redemption on JL between the U.S. and Japan/Korea.

If you are interested in getting 60,000 AA miles after one purchase of any amount, here's the link to the current Barclays offer:

https://www.applyaviator.com/

I suspect that there are some times when you can get a one-way Business Class redemption between the U.S. and Asia with 100K Amex points -- maybe with very high carrier surcharges. The problem is that you have very specific requirements: You can only travel during a particular time of year, and you only want one connection. The more restrictive your travel requirements are, the harder it will be to find reasonably-priced redemptions.

If you are willing to make more than one connection, I would look at redeeming BA or QR Avios for QR's SGN-DOH flight, and then looking for DOH-ORD (perhaps with a London connection) on QR/BA. BA is a transfer partner of both Amex and Chase. BA Avios can be redeemed for travel on QR, but can also be transferred to QR in the event that QR offers a lower redemption rate on a particular itinerary. Watch out for the carrier surcharges.