An unhurdled slip-and-drop would be fatal without a doubt.
If this is the case, then maybe you need a belay. However, if the snow is sufficiently deep and soft that you're sinking up to your knees, why is it the case that slipping and being unable to self-arrest is so dangerous? In these conditions, typically you can't even intentionally get going fast enough to glissade or practice self-arrest.
Given the conditions you're describing, the first thing I would worry about is avalanche danger. If the snow is that deep and soft, it sounds like you've just had a storm dumping a ton of fresh powder. Typically there is significant avalanche danger if there's (a) a lot of fresh snow, and (b) a slope of about 30-35 degrees or more. Since you're describing a slope of "nearly 30 degrees," I think my basic answer is that you should not be out in those conditions due to avalanche danger.
I would not suggest going out and then making the decision about whether conditions are OK to go up. There has been a lot of work by social scientists studying why people die in avalanches. Avalanche safety courses and transponders are not really highly correlated with survival. Once people get there, there are strong social forces pushing them forward. See Ian McCammon, "Evidence of heuristic traps in recreational avalanche accidents," http://www.snowpit.com/articles/traps%20reprint.pdf
Obvious Assumptions: I have walking sticks, equipment, Ice axe.
If the slopes are a little less steep than you're describing, or there's not as much fresh snow, then the avalanche danger might be acceptable, and then these are conditions where you want snowshoes. Personally, I don't bring poles when I'm going to be on snowshoes; I just bring an ice ax, which I only use if I'm on a steep slope. For mountaineering, you want snowshoes that have crampons.
As far as routefinding, you have various options, the most straightforward of which is not to march up to 22,000' in the middle of a storm. If you find yourself in whiteout conditions, you could try to use GPS, but since GPS isn't 100% reliable, I wouldn't intentionally seek out conditions where you were likely to need it in order to get down from such high altitude.