In reply to mars:
We went up Hall's Fell yesterday - a great short day out. I'm not a fell runner so I can't be certain what it would be like in trail running shoes, but we and other parties on the ridge were not using crampons not felt any need to. The snow cover is well broken now but you would find it difficult to avoid snow entirely on the steeper sections. Keeping to the ridge rather than the paths that run below the ridge was more snow free but I'm not sure that would be your preferred option. As far as the snowed up sections are concerned, I guess it will depend on the temperature when you are there. It was above freezing for us, so the sections of compacted snow on the paths still had some "give" in them - not really icy.
We came down Doddick Fell - generally easy, but there was a short steep descent on snow at the top - big footsteps but I was glad of my walking pole - didn't bother with the axe. This was trickier than any of the snowy bits on Halls Fell, but very short and a slip might not have been as serious as in places on Halls Fell.
The iciest bits were on the summit plateau, but I guess you'll be expecting that.
Hope that's of some hope - good luck with the "Round".
Martin