Jon's words being said, let's clarify that it often happens to be that most awards on partners tend to be greater than on the host program's airline itself.

That you mention EVA, you might want to consider outright booking their Evergreen Deluxe Economy class. I'll let whoever is so inclined to do the search and post the links, but in a nutshell, it's a business-class seat at the front of a 747 for a few hundred dollars more than a ticket bought at bulk fare. One of the best values in the air, in my opinion. Check it out.