I'm not sure why box2d is so jittery sometimes. Roughly, as I understand it, the way physics sims work is it moves stuff around with gravity and forces, then it loops over all the constraints (collisions and joints) to resolve them. It does that loop multiple times. The higher the iterations the closer to perfect it will be. In the case of rope with infinite iterations it should in theory be a perfectly stiff rope that doesn't stretch at all.
Anyways, aside from iterations you should be careful with vastly different masses, that also can make things more unstable with something like a rope. As least from tests and what i've read. Your other issue of the rope being pulled through smaller pegs may be helped by links closer together, bigger pegs or even using segments instead of circles for the pieces of rope.
I did this event based rope based physics to test some stuff out. It's probably much slower than box2d but the results are pleasing to me. The length of the rope is limited as you drag the rope around. Some things such as the pinned end and that it only works with one rope are hard wired in so far.
dropbox.com/s/8vobbfougch0edt/verlet_rope_test.capx
Here's also a quick modification to make it similar to you c3 project. The end is moved with the 8dir behavior and it's momentum is set to 0 so it kind of drags behind if the rope gets momentum.
dropbox.com/s/c7ikyff1z4b7mtl/verlet_rope_test_8dir.capx
Not sure either are useful. They are mostly just tests for fun. The first half of this post is the helpful part.