Since this is a plot point that has been constantly debated throughout the entire run of the Stargate franchise, here's something I would change:
Make the Stargate public knowledge from the very beginning, and actually allow the world to react to the news instead of keeping it a secret the whole time.
That's the kind of thinking I'd want to see from the people I hire to reboot it - don't get hung up on preconceived notions about how a show must be this way or that way. Be daring or don't bother. Maybe that's not the right approach but someone needs to give it a good think-through before coming to that conclusion.
really isn't an "idea" guy so much as a "trash everyone else's idea" guy.