Thanks for all the good information! I decided to book a later flight to Taipei. I am arriving on AA 175 at 2:05pm and connecting to a JAL flight that leaves NRT at 6:35pm to Taipei. It's all on the same ticket. I guess that means I'll be at the Admirals Club for a few hours.

On the return flight home I will be arriving in NRT at 4:55pm on CX connecting to AA 154 at 6:45pm. Hopefully it all works out.