We won against sea of sorrows...two weeks ago? Exact same situation you described.
Also, it's obvious that TC's morale does get hurt. You easily have 3 to 4 times as many people out there now that you are winning, as you had out there while BG was winning. I'm sure you have a dedicated core whose motto is "Never give up, never surrender", but last week between 60 and 75% of your server had just given up, as evidenced by the score.
This isn't an insult, FA is in the same boat. Even more of our players gave up in the BG matchup. We were even farther behind in score than you were. But the point remains: the vast majority of people do get discouraged and give up. I think all servers are in this situation. I think game mechanics are designed and the information presented seems expressly designed to encourage people to give up. I don't really blame the players so much in this instance as the game.
Once one server has a lead and all the orbs, people conclude it's impossible to take first place, and get demoralized and stop showing up. It's probably, beside transfers, the single biggest contributor to unfun lopsided matches.
I don't think TC is winning because they got huge zergs of transfers, I think they are winning because they have the strongest night presence and so people woke up and saw TC with a lead, all the orbs, the upgrade advantage, realized this would happen every night, and just gave up.
I'm almost thinking they need to have several borderlands, one for each 'time zone' which is open for a specific amount of time during the day and then is locked.