Dear Idea Person,
A lot of tough love on this one!!!
Here's the deal - ideas are the most common thing on the planet. Ideas are basically worthless until they are proven practical. Take it from me, I'm a crazy inventor who has had to learn this lesson over and over again.
Here are some strategies:
1. Get them to sign a non-disclosure on the idea (this probably won't happen because big companies say 'you are not giving us any ideas we do not already have'. And they are usually right!
2. Make it look like a full product or service and sell it. Get the order and then build it to suit them.
All big businesses are in the game of taking other peoples' ideas and profiting from them. But you are wrong in thinking that they want to squash you -- they have no time to even think about that. That is your fear for not taking action. Ideas and business models get "stolen" all the time. Big investors will never sign a non-disclosure for the very fact that they might "already" be working on your idea and would want to avoid any legal troubles of signing to hear your "idea".
If you are going to approach a big company, put in all the footwork first, get your intellectual property protected.
Why not contact 1,000 people and pitch your idea. Maybe some one will steal it. Maybe someone will deny you. Maybe someone will say, "we love it, how do we start?".