I also use half semolina, half AP and get good results. The semolina flavor still comes through just fine, and the dough is very easy to work with. I confess to using my KitchenAid mixer for mixing and the preliminary kneading, and then use the roller/cutter attachment for the final thinning and cutting. It's just so easy with the extra height and having both hands available to feed and catch the dough.
The whole idea of letting the dough rest is to give the gluten that has developed a chance to relax. Otherwise, as OregonYeti points out, the dough will be impossible to work -- just like pie crust dough that hasn't rested.
And another hint that I learned through sad experience: if you're not going to cook the pasta within a short time, DO NOT cover it with plastic wrap right away. It will get too sticky and be a mess to cook -- especially bad with filled pasta, since holes will develop when you scrape it off the surface (floured parchment paper, in my case) and you'll lose a lot of the filling.

Give it a chance to dry first.
I recently got hold of some fabulous eggs, from REAL free-range chickens that scratched around the farmer's main vegetable fields. The yolks were the deepest orange I've ever seen, and the pasta I made with them was
deep yellow like this! I used about half to make ravioli, and the rest is in sheets in the freezer for another use. Which brings up another question: Has anyone thawed out frozen pasta sheets and them rerolled them to make them thinner? I'm afraid they'll be either too dry or too wet to work.