How would you do it if you were to launch a landing page in 24hrs?

I would make sure I have a community of supporters behind the product too.

I'd focus on the copy and ditch the rest. Whatever the reason is to launch such a page in such a short amount of time, best is to focus on what moves the needle: copy. Actually, this would be a great project for any team: remove any kind of design on your homepage, and focus on the story you want to tell.