Quite frankly, this would be one of the better Star Alliance redemptions out there using A3 or UA miles in business rather than Avios. There is no direct OneWorld routing making it much more expensive using BAEC and Avios.

For cash bookings I have always found tickets originating mainland China to be excessively priced as well as hard to purchase from outside the country. Credit cards often refuse to authorise such purchases. As previously posted, your choice would be on CX or MH. Normally that would be a simple decision, but HK does seem dodgy right now and could potentially get significantly worse IMO.