Good to see some thought going into this topic MD.
In my experience, when the weather hits, the wind generally prevents you from doing a great deal with any makeshift shelter. I would be fairly hesitant to try any kind of tarp at all unless it was more in line with a Bothy bag or proper Bivy.
Trenches would be my absolute last resort If I couldn't find a drift or general depression behind a boulder etc. Digging into drifts has another set of problems due to the large accumulation of snow on the Lee side. You have to be very vigilant to clear any entrance of the shelter you create.
Doing anything in wind can be extremely difficult and IMO it's best to spend the time on the shovel in building a more secure shelter. I've spent an hour working my way around a tent during blizzards before only to get back to the start with the same amount of snow built up. When it comes on strong, you can be buried in a trench within 10 minutes.
I've spent 15 minutes to build a rough hole and ledge in a drift to sleep on, and also spent 2 hours building snow caves to sleep in. If you know what the weather is doing and new snow is not in the forecast then it's probably ok in terms of trenches with tarps etc. In this case though picking a spot you know won't accumulate is critical. Set an alarm if you're unsure to check you haven't been buried.
Most of my bad weather experiences have been above the treeline in big wind so I tend to have my own specific kit and rules.
In terms of shovels, I have two options. My Blackdiamond Bobcat has a large blade which can move higher volumes of snow and if I'm going fast and light, it's the one heavy piece of kit I take. All the small light flimsy shovels I see around are pretty useless when sh$t hits the fan. When the weather is good I'll take a smaller version.
I'm always experimenting with cheap and light Bivy's, sometimes with success....sometimes not.