Could you access the bypass and skip the lower butt?
I haven't climbed the NEB, but it looked like either start was possible without crossing any ice. We viewed the 'glacier' from various points along the trail and there really wasn't much left of it. Compared to how it looked a few weeks back it's tame.
Having said this, everything was active up there on Saturday so a quick and early crossing by headlamp would be the way to go.