Thanks, everyone.
Yes, we arrived almost two and a half hours late. Missed the connection...not even close.
What ended up happening was there was tons of TG staff at the gate fro probably every city where people missed connections, with the alternate flights we were to take. For us to Taipei, we were surprisingly booked on the CI flight at 10:55, which was probably about the best outcome from a time perspective. I'll leave comments about the ratty old 747 interior, etc, because I really was impressed that they had it all so organized and everything ready. The staff then escorted us to transit security and the CI transfer desk to get new BPs etc. But with the length of time it took, our 2 hours was basically doing those formalities. Then over to the new gate.
I was thinking they would prefer a *A flight on EVA. The 12:00n flight was full, there was still a 2:40. But glad they got us out as fast as possible.