The reason we think of Peavy as being at best a 6-inning pitcher in the AL is because he was a 6-inning pitcher in the NL. Over his career he has averaged 6 1/3 innings per start. Thats while playing in a terrible weak NL west, with a pitcher slot, and in Petco.
Look at what CC did to the NL last season. He's always been a great pitcher in the AL, but he absolutely destroyed the NL. Same thing with Clemens. It's no secret.
I like Peavy, but I have watched a lot of his games (my friend is in love with him for some reason), and I don't think he could be anything great in the AL East. You would be looking at a 5-inning pitcher, unless he drastically changes his pitching approach. I would compare his style almost to dice-k in the sense that when he gets an 0-2, often it will end up 3-2. He just throws WAY to many pitches per at-bat.
That being said, I would love to have him at a cheap price, but they should absolutely not overpay for him. If he could learn to be more efficient, he could be great, but I think it would be just too big a gamble to give up a lot of talent. I don't think I'd want to give up even 1 top pitching prospect for him.