Very true Twee! Our group (3 of us), summited the same day (Mon, 06/18) and we had the same moments that your report mentions.
We started at 3.30 am, and the icy patches on the switchbacks were very slippery. At times, we were using the ice axe to break the ice on the trail to get a better grip. We did carry crampons, it was too taxing to put them on and remove them for the occasional patches, and walking with them on for all the other rocky parts of the trail would have taken a toll on our knees. As of the snow patches, since it was a cold early morning, neither could we kick in steps.
I have climbed the shoot last year, but this time, one of us was a first timer, so preferred the switchbacks.
Apparently, I think the mistake on our part was that we came prepared to climb the shoot, but not the switchbacks. Microspikes would have been easier to use.
