I'm sorry to hear your bad experience with EVA Air's online booking system. I, personally, have not tried to use the system. However, when simulating certain routes, like ORD-TPE, I've had difficulty actually finding a fare. The system is very limited at booking itineraries with multiple legs.
I suggest you contact a travel agent for your travel plans on EVA Air. The travel agent may have lower fares, although the EVA Air website does sometimes have lower fares. The generous booking bonus is also a plus.
Happy Flying!