We deal with this issue at The Economist and in the past couple years, we've been able to implement some lean thinking to move things along faster.

At the core, what you're trying to change is the culture.

Culture has 4 components that a group of people (people in your org) share:
1. Value system (what they consider important)
2. Belief system (how the believe things work)
3. Behavior (habits, rituals)
4. Artifacts (manifestation of the above)

You need to start addressing the first 2, then you'll see the progress (or lack thereof) in the last 2.

Here's an example: a bad approval process that makes product development move really slow. We discovered this happen because the stakeholders want to show that they're contributing to the project. Because of this, they want to make sure they get to review the project and give feedback. This way, they can show their contribution for the product's success and this would be good for their performance review.

From this example, the value for these stakeholders is recognition. Their belief : giving feedback (even if it's superficial and immaterial) shows that they're contributing. The behavior: blocking process in order to get a chance to give feedback. The artifact: feedback for the product in email, request to do reviews, meeting invites.

How to start:
1. Find your allies. These are people who also want to move faster. Ideally people who work in your team
2. Show real value. The reason why you want to work fast like a startup is so you can deliver value to your customers faster and more often. What can you do to give other people around you (who you want to influence) a taste of what that's like? One thing that we did was to do rapid prototyping (without code) and do usability test, then shared the video highlights with the stakeholders.

I'll be happy to share with you the way we did this at The Economist mobile team and offer some actionable ideas to help you move forward with the transformation.