Watch some of the Youtube videos of it. The tough part is best suited for short-wheel base Jeeps/Toyotas. I've no doubt the Cruiser can do it. But there's a high risk of body scraping/damage. The toughest part has NO ROOM to turnaround if there's oncoming traffic.
I've told this story before on this forum. My wife and I were walking part of the northern side when we saw a very expensive Mercedes SUV coming from the Marble direction. The side of the vehicle next to the rock wall was severely cut, scrapped, and ripped. Windows were broken, the mirrors were gone, and almost every window was cracked or busted. They were tourists from out-of-state in Denver for a work conference. They decided to head up to Marble and venture on Schofield pass without doing any research. One guy was driving , the others were walking. They were all freaked out. Some of the damage occurred because they lost their focus and did not drive by controlling their fear. The other damage occurred because there are some tight spots on it.
If you take your cruiser, I'm sure all of us would love to hear a trip report.
I've done a lot of 4x4 trails in CO. This is one I won't do in our Cruiser. To each his own.