I think the best FF program for you is UA/CO. Both Eva miles and Asia miles expire after three years from the month the miles are earned. To get a coach award ticket to SGN on Eva, you need 100K miles for normal season, 150K miles for peak period, which covers lunar New Year. And it requires 110K miles to get a free coach ticket to SGN on Cathay. It is not efficient for earning award tickets on Eva or CX.

For UA/CO, you only needs 65K miles, and I can see available awards now for, for example, SFO-NRT-SGN or SFO-ICN-SGN, around lunar New Year next year, using continental's website. With UA/CO miles, you can redeem miles for flights on Star Alliance partners, like ANA or Asiana. So it is not as difficult to get award tickets as you think if you plan ahead.

If you purchase tickets, UA also has flights connecting in Hong Kong, which should be efficient too. So you might want to see if you can put your Eva miles in use first, then start accumulating miles on UA/CO. You can get credit cards, with big sign up bonus, that earn or can be transferred to UA/CO miles, like the upcoming UA Mileage Plus Explorer, CO Onepass Plus, or Chase Sapphire Preferred card. You might also consider getting the Amex Premier Rewards Gold card for the 75K bonus and transfer the bonus points to CO miles before their partnership ends by 9/30. After that, you can transfer Amex MR points to Aeroplan, which allows you to book award ticket on Star alliance too for 75K miles.

Also, you can use UA Mileage Plus shopping website for online shopping with any registered credit card to earn bonus miles, which helps accumulating UA miles faster.

So i would suggest you check out the Continental website for award availability and see if it makes sense for you to accumulate their miles based on your need.