Mid-December to late December is the top season as Taiwanese in the US/Canada return to Taiwan during their school breaks. I also find that EVA, for good reasons, does not release Kitty Jet inventory as generously as other flights.
The suggestion to do intra-Asia is a good one. One can even do something like: LAX-TPE-HKG-TPE/TSA-HND-LAX so you get 4 flights on Kitty. HND-LAX on NH. The problem is that I think UA would not allow an award ticket with both a stopover in TPE and the TPE/TSA airport switch. So, you might want to see if you can pay for TPE-HKG-TPE.
As TPE-LAX go 3x daily and TPE-SFO go 2x daily and 3 new 777s getting delivered in the next few weeks, inventory might open up. Still, Kitty jet will be the last one to open.
Of course, the Kitty does not end on EVA. Also take the Hello Kitty Gondola:
http://english.gondola.trtc.com.tw/c...0772&mp=122034
In the metro, you will see the United Friendly ads but also ads for Hello Kitty Vitamin C and, get this, Hello Kittty Chicken Soup! Cat sells bird soup