I did it solo and on a day permit as well. You don't need any technical or professional skills to get up the chute. It does look daunting at first, but very doable if you take your time and just take one step at a time. I had on crampons and ice axe, but I didn't use the ice axe until I got closer to the top of the chute as I relied more on my hiking poles. Also, when I went, the path up was literally carved into the snow so I used those path as footing heading on up.
It did take me about 2.5 hours to complete though and fairly steep. In fact, from Trail Crest, looking out, you don't even see the slope, looks as though it's a vertical drop but it isn't.
Trail Crest to Summit, was clear and dry, but I struggled at this section. Almost wanted to turn back too. The limited air just sucked the energy and desire to complete... but I finished
I did this on the 17th - not sure how it is today as I know snow is melting quickly.
