Like I said, building a high enough bridge. I'm pretty sure all maps include a tall structure on each island for this exact purpose. You can build high enough to avoid his tnt cannon, and shoot him down if he tries building as well. Whether you succeed or fail isn't the games fault. Sometimes you win, sometimes you lose.
You all could also have gotten power bows and spammed him back, or at least had 2/3 spam him while a third snuck around and built from the side or high up.
He did because he stayed all time farming diamonds safe and warm in his room and getting stacks of Notch apples which made him immortal.
Again, he was 3v1! You can't honestly expect him to make the move to you. A team of 3 people can strategize more and have much more probability of winning. The rage quit and bad luck with anti-cheat aren't your fault, but they happen.
We tried and he either shot us, blew up our bridge or he fell and took no high damage.
In that case, either your bridge was not tall enough, or you didn't have a shield to protect yourself. Both of those are easily solvable, and would have voided all of your scenarios.
-A shield will protect you from him shooting you.
-A tall enough bridge will prevent him from blowing it up.
-If he fell and took no fall damage, he wasn't high enough which would mean you could have built during the time he was re-building up, or you weren't high enough to force him into taking fall damage.
Late game in Eggwars is all about outside-the-box strategies. You just have to be able to come up with one that works!