I foolishly attempted this years ago on snowshoes before having enough avalanche training and experience. Thankfully I turned around as I just didn't have the skillset to assess conditions.
Getting down from goat mountain to the col, and then up is doable, but has numerous high risk steep slopes. While there are trees, a small slide could push you into serious terrain traps that would have extreme consequences.
Climbing up crown would have less risk at first, but there are several slab patches that create perfect avalanche conditions as it's a slippery bed surface on a steep angle. High probability. There are several conditions it may be lower risk, ( last January had a week that would have been good) but you would need:
1) Avalanche Safety Training 1 - bare minimum to assess if the conditions are the same as listed in the forecast.
2) Low/Low/Low avalanche forecast
3) Mountaineering course - Ice axes and crampons are counter intuitive to learn how to use, hence why many use them incorrectly ( they tend to be the folks without helments). Most assume this isn't the case until they take a course and learn all the ways it's easy to injure yourself.
4) Lead climbing experience - Might be worth roping up for the avalanche sections to reduce risk of being pulled into terrain trap.
In general it's tricky, but doable if you have the right skills and conditions.