The nice side effect of being a contractor is that your CV now looks like you have been in the same position for 10 years instead of a series of 2 year stints.
I have done this and always worked hard to help the team succeed. Later, when I decided to try working for a couple of large companies, I was stunned to be treated as "you work in my organization and will follow my every whim".
One example is attending endless pointless meetings waiting for the client to decide what spec they want, just because the manager wants to everyone on the team to be present (and silent). As a contractor, it becomes quite easy to say "it looks like I am not adding much to your project until the project spec gets settled. Please let me know when you are ready to implement (or have more detailed questions that you need to know to flesh out the spec) and I will be happy to help anytime". In my experience, it is quite common that they will have hashed out the requirements and be ready to start work after 12 months or so and were happy to talk then.