On people dying even though the wall is down: The logic for walls going up and down, and the kill teleporter spawning and despawning are the same, so there is no delay between up, and spawn, which may have been the issue when crossing. You wouldn't see the wall come up before you get teleported. There's a 5 second window to cross. If I need to, I can lengthen it. If you did indeed get teleported when you should have been able to move forward, then perhaps the spawn/despawn scripting is unreliable. The other possibility is to remove the spawn scripts for the teleporters and delay it a second after the wall moves up.
Side note: 343 should consider using my map as a stress test for their scripting system
On winning a round unexpectedly: Did it happen at the beginning of a round? That would have been because they pushed the other team off the stage entirely during the last round. On that condition, the team the pushed all the way wins the entire game.
If not, the likely culprit is one team pushed the other team back 1 second too late, the timer to end the round completed, and even though the team got pushed back to the center, they won because the push script hadn't yet completed to set it back to neutral. Again, that's speculation of expected behavior, but if the scripting system simply bugged out, I have not control over that.
On communication: Agreed. Going make a rules sign, and put it up for the start camera.
On 3 strongholds: That I don't think would work. If a team has pushed once, then the other team would still be contesting the territory, but they'd also capture the territory at the back of their base, leading to the team which has been pushed farther winning. Even with two to score, I'd still have to teleport one of the teams out of contesting. It's simpler scripting wise to just teleport you to the stronghold.
On Jumping: That might make it simpler, and it's been suggested before. Grenades blowing you up and over the barrier would still be an issue though.