I think 11mm is probably overkill. Get it wet and iced and good luck loading it into most modern belay devices. I rapped synchronicity on two fat singles like that and I had to run face down psuedo-aussie style to get the frozen ropes through my device.
Have crampons and tools REALLY been demonstrated to cut ropes in a catastrophic sense, in a practical scenario? I.e. Spearing the rope with a pick or front point leads to the rope parting then and there? Most likely scenario to me is that you accidentally pierce the rope with a tool, it doesn't break though at worst gets a core shot or bad sheath damage, so you just chop that section off. If damage is from tools then it is necessarily close to your tie-in.
Wasn't there a UIAA test recently (last 2 yrs) where they stomped all over ropes and crampons and determined that the ropes were not damaged to any level requiring immediate retirement?
edit to add link: ACC safety articles
following my own logic I conclude that the best choice is a longish single skinnyish rope.