There was some confusion on FlyerTalk regarding the amount of miles needed, as some phone agents were telling people that there was a separate EVA Air award chart (possibly the old Continental-EVA partner chart) that required substantially more miles to Taipei (50,000 miles one-way in economy) and no combining with other partners airlines on a single itinerary. However, that issue has now been resolved. I had a booking to Taipei over Christmas, with my original itinerary being SFO-ICN-TPE. I was able to call in and get that changed to a direct SFO-TPE flight on EVA Air, all for the same amount of miles required on their partner award chart (32,500 miles one-way in economy). Taxes and fees for this one-way award totaled only $2.50! Although if you book a return flight, the cost will be slightly higher since it would include a Taipei airport tax as well as U.S. Immigration fees.
Confirmed EVA Air ticket booked using MileagePlus miles
The biggest headache, however, was finding an agent who actually knew how to search for and book EVA Air award tickets (or an agent who's even heard of EVA Air for that matter)! In all, I called a total of six times to get my itinerary changed successfully. Out of the six, only two of the agents were able to find the EVA Air award availability, and both needed their supervisor's help to get the changes completed. It might be worth the hassle though, since availability seems to be fairly open in economy even during the holidays, and there were also Premium Laurel (business) seats open on many dates I checked. If you get an agent who insists there is no EVA Air award availability, hang up and call back again.
Best of all, EVA Air recently announced their new Royal Laurel Class, featuring lie-flat business class seats in the same mold as Cathay's reverse herringbone design from Cirrus. In fact, they are supposed to start operating on the JFK-TPE route this month, and LAX-TPE beginning September 2012. EVA Air offers plenty of one-stop connections to Mainland China as well as Southeast Asia via Taipei, so having this additional trans-Pacific lie-flat option using MileagePlus miles is a huge plus. I'm slightly wary that award availability will quickly dwindle once EVA Air becomes fully integrated into Star Alliance and online booking begins, so my suggestion is to book early if you plan on heading to Asia within the next year.
EDIT 12/11/2012: Lucky over at One Mile At A Time has written up a good synopsis on how to search for EVA award availability. However, I would still call up the United Alliance Desk (877-726-7282 Option 3) to make the actual booking. The agents at the regular award desk remain hit-or-miss when is comes to familiarity with EVA bookings.