He is only a week late, I would question why the rush to get him out, is he getting too big or causing you issues. I had both mine with different OB/GYN groups and both went by the 2-week late, then induce way of thinking, unless there was a good reason to take them early. Anyway-
With my first-five days late-36 hours labor start to finish. I was in very hard labor but it was not dilating at all after 5 or 6 hours of contractions that were 3 minutes apart. I was given an epidural first then the pitocin. They had to break my water and it stil took another 10 hours for him to arrive though there were other things going on (he was very high, cord wrapped, miconeum n fluid-spelling?) etc. I had back labor, so I could still feel my legs, when I had to pee, all of my back contractions, but it was bearable.
With my second, I had my first contraction at 9pm, he was born at 1:05am. No epidural, nothing at all-not my choice, only because they "didn't have time". I had back labor again and didn't think I could get through it.
Two very different experiences except for having back labor and the meconium thing for both and o yeah, the ripping thing for both as well.
If you are open to an epidural, I would go for it and not worry about the pitocin too much.