If you're 100% certain that the people interviewing you will be people who already know you, then the first impressions were made long ago, and you'll all have the advantage of knowing each other, their personalities, and everyone will have a good understanding of what everyone else is capable of. Thus, the types of things you'd normally do for that first impression may not be as critical as if you were walking through the door for the first time.
However, you may find that someone wants to interview you who doesn't know you. Perhaps a senior level executive or someone else with a stake in the hiring decision. In this case, being prepared to make a good first impression will be helpful to not only you feeling comfortable but for everyone else to feel comfortable knowing you have good judgement.
My suggestion isn't to overdo it though. I wouldn't suggest treating the interview like casual Fridays, but perhaps being too overly formal might be too much. The key is to dress how you would feel comfortable if that senior level executive were to meet you in her office while at the same time not making yourself uncomfortable around your colleagues who might not normally see you in your formal attire.
Since this is a larger company, you may know of other former contractors who have interviewed for a permanent position. You might consider asking them what they did so that you can determine what the company norms are, as they may differ from company to company. This may help you decide what level of formality would be right in terms of what's expected and what you're comfortable with.
In the end, the answer likely sits somewhere between your normal, everyday attire and your first interview formal outfit.