First of all, eggwars is a team based game where you are supposed to trust your team mates. Anyways, In mot cases you'll be playing with your friends, and this will give you the advantage of faster communication. This will also ensure a team where no one will just suddenly leave you alone. It is possible to win by yourself in a multiplayer map depending on skill level,(my team got defeated once because we thought it was fine to leave one player just for fun) and no player can be constantly watching multiple players. They'll have to go get supplies (arrows) or it's totally meaningless for them to just be watching you. What can they do, stalk you to death?What if you're alone and the other team isn't? You won't even stand a chance.
What if the player continually watch you? no way of getting around.
Also, not all mid's have multiple diamond generators.
How would going under the island help? going from above is reasonable because you could jump down, but because you can only break blocks placed during the game, going under the island isn't quite practical.
As I said somewhere in the thread, diamonds won't help you getting to their island.
Of course it's possible, but it's very hard and takes very long. It's not fun. Enderpreals could be the solution. It would improve the fun and the gameplay.
Also, if enderpreals are really not an option, do you have any opinions about levitation potions?
I can already imagine an argument saying "but what if I don't got friends to play with and I'm by my self?" (no offense) In this case, adding ender pearls can be a possibility, but giving players enderpearls will cause a lot of unfair destruction of eggs/kills. It's probably impossible to add a plug in that allows you to buy enderpearls when you're only one person on the island either. Giving players that are by themselves ender pearls can give them an unfair advantage, allowing them to run away from island to island much faster then the other team.
Anyways you can go to the bottom of an island by placing blocks around the island, and I have found this quite effective when playing. Heres a picture of when me and my friends were playing in 1.8.9, you can see my friends making bridges from the bottom and top. (if you don't already know about it)
(IT'S LATE I GOT GRAMMAR ISSUES)