Did it tell you to use a smaller needle for the ribbing? Normally you do use a couple of sizes smaller for ribbing around a neck edge and on the front bands of sweaters, so it seems you would do that here too. If you have done that and it didn't work maybe it is because you have more stitches than would "like" to be picked up. You could use just one size smaller if need be, but I'd think you should probably use the ratio they suggested (1 or 2 sizes smaller than the body, or whatever they said), unless it's wacky.
I know from reading your previous posts that it told you a certain number of stitches to pick up. I'm not telling you what to do, but here is what I would do it I had to pick all those stitches up. I know some of the stitches are live and you don't have to pick them up per se, but just start working them off of the needle you held them on. On the live stitches just knit them in the K2, P2 rib pattern (or maybe you work one row in just knit before you start the rib?)but when you have to pick up the stitches for the rest of it, I'd throw the number of stitches they suggest out the window and pick up what needs to be picked up.
I went to a finishing class and the instructor said she never pays any attention to the number it says to pick up. Well, you pay a bit of attention to it,
in that if what you pick up is way, way different there may be a problem. And in this case since you are working in a circle and have K2, P2 rib you need to end up with a multiple of 4 so the rib will fit in properly. (That is paying attention to it too.)
On vertical and diagonal sections you need to pick up 3 stitches and then skip one all the time. That ratio makes a nice flat border most of the time. 1, 2, 3, skip all the way until you come to your stitches on the needle, then work them and then go back to 1, 2, 3, skip when you are past them. The fact that you need a multiple of 4 makes it a little harder. If you have to fudge a little don't do it all in one place, spread things out over a long distance if you have adjustments to make in the normal 1, 2, 3, skip sequence. Or, I just had an idea... if you picked up what needed to be picked up and it was a little off of the multiple of 4 you could ditch the few stitches you were off on the next row by working 2 tog spaced far apart and in as inconspicuous a placement as possible.
I know these kinds of things can be a nightmare sometimes, but since I started picking up what needed to be picked up and have forgotten the "number" given, I have found it fun. I can't guarantee anything since the needle size may be part of the problem, but my bet is it isn't that so much as the number of stitches. Good luck.