Okay–I think its time for me t step in. Stop using cotton string. Move onto 50/50, or Polys.
Now, the yoyo you have is good. But if you need a metal, according to your preferences, it seems like the M1 or the project fits your diameter needs. Now, the width that you want is almost PERFECT with the M1, but the Project is a little wider. It seems like the M1 has everything you need. They come with silicone pads, but you can also use k-pads in them, however, I would recommend chaz pads, or just plain silicone a bit more, cause IMO, they are better then K-pads.