I don't recall there being a production error in the Empress Theodora run? Unless you're referring to the elevator stalling for Josh, that was not a production error at all. He took his hands off the actuators that operate the elevator, which is why the elevator stalled and the team came up short of the artifact. If he kept his hands on the button, perhaps he could've reached the artifact. Or if Ashley moved faster in the temple.
For the Golden Cup run, there is no doubt in my mind that this run would've been much better if there was no production error in Room of Harmonic Convergence. Katherine was moving pretty fast in the temple, but losing all that time in the Harmonic Convergence hurt them. Also, Sean ran into a production error in the Treasure Room. This was one of the most unluckiest teams on the show. Not only was their original temple run postponed, but their new temple run was riddled with production errors. After the Discarded Seal team, Katherine and Sean deserved a second chance in the temple no questions asked.
Also, you can add the Lost Logbooks and Golden Stallion run to your list too. Lost Logbooks had the production error in Harmonic Convergence and Golden Stallion had the Throne Room error.