Have you contacted any of the companies to ask about how they approach royalties, IP and pay structure? If the idea is fully mapped out and ready to go, and they like it, do you plan on licensing them the rights (you own the IP) to manufacture and sell your product for the royalty payment for x timeframe, or sell the entire idea to them (they own the IP) and then claim a royalty on each unit sold?
If you really think that you’re onto something, then I’d call and ask all of your questions so that they are expecting it before just dropping it into someones inbox and hoping that it’s the right one, that whatever it is is protected and that they actually get back to you. I’m sure that this would be a daily scenario for big brands.