Several of those are very similar large cities. Unless you NEED to be in each one I would probably pare the list down a bit as that is a lot of hopping between places in short amounts of time so you'll be spending a lot of your time in airports and getting to/from airports.

Using your AA miles for CX J class makes sense to me. Yes, I would travel in one direction and avoid jumping back and forth. TPE and HKG are not especially close to the other places (but the 3 hour flight from that part of Asia to SE Asia isn't terrible).

BA Avios can be good for these short hops so you may consider transferring your MR points to BA. They frequently have bonus point transfer offers so I would probably wait and see if anything like that pops up. TPE-HKG for example only costs 4500 Avios in Y on CX. And there are about a million flights per day on that route so finding a seat should be easy. The problem may be finding OneWorld partners with sensible flights between some of those cities.

Of course you can also transfer your UR points to UA and fly *A carriers which are plentiful in that part of the world. But they require more miles than Avios on comparable routes.