The key is going to be for you to methodically lay out how the skills you used at startups translate to the corporate world.
What you're fighting isn't reality, but perception. So it becomes a translation job to get the corporate-types with whom you are interviewing to understand that you do have skills that work well in a big company.
But skills are also only part of the battle. The other battle you'll need to fight is culture and the perception of culture. That perception is that startups often tend toward a "fly by the seat of your pants" mindset and a general lack of discipline. I realize that's not always accurate, but it's a perception that you're going to fight.
Another perception you're going to have to overcome is that people in startups don't know how to "conform" to the corporate way of doing things, especially in very large organizations. The reason is that they want someone to come in and do work their way, often which is dictated to them. Most teams in large organizations don't want someone to come in and change how they're doing things and that's one way people in startups are often perceived (which gets back to the "seat of your pants" perception above.
When you talk to recruiters, tell them you're looking to transition into corporate. Most (in my experience) will help you develop the right presentation.
Lastly, network, network, network. Get to know people in organizations for which you'd like to work. They can help you with referrals and let you know when their organization is hiring.