Our group of four is back. Three of us summited, one stopped short about 1/4th mile from the summit.
I have two take-aways:
1) Don't underestimate the trail between the Trail Crest and the peak. We assumed 1.9 miles should be easy compared to the snow chute, but it was certainly not. After taming the 600m of snow wall, even horizontal hiking at 4000m altitude is no fun. In this case it is not horizontal - it goes both up and down. Mostly up, of course. We took 3.5 hours to go from trail crest to the peak. Two of our group developed light AMS in the middle of the trail, having no indications before. One (wisely) decided/was-convinced not to summit, another summited, but was quite disoriented, spacing out from time to time, and made us all worry.
2) Crampons are designed to be used on ice and on hard snow. In the upper part of the chute the snow is harder and perhaps can get icy, so please do bring crampons and axe. That said, about the 2/3 of the snow chute's lower part the snow is soft and the foot gets in to the snow easily over the ankle. I found that in these conditions kick-in climb works better and saves energy. Axe is still helpful in case you need to self-arrest.
The same day, on July 3rd, I think the last to summit was an Asian-looking girl. We passed her on our way back and it seems like she should have made the summit, if she continued, at 3:30-4PM. At around 7:30PM she was still somewhere at the mountain and we did not see her on the chute. Does anyone know if she made it back alright?