Well you got me all excited thinking about my DST so I went out and braved the Seattle heat wave to show you the pitches I'm most familiar with. I'll try and explain them as I go.
As I mentioned above. . this is my go to pitch 90% of the time. I can have it up in 120 seconds. It's really versatile on variable terrain. It sheds modest rain and wind well. It provides PLENTY of ventilation. More than enough sitting height. Almost a bit of a porch so running my emberlit stove is not a big deal. Hell I've even used my little titanium SO box stove with the chimney angled away from the door (just for ambiance and to cook).
View attachment 55133
Modified A-Frame. I use this whenever I know it will snow. Note the steeper roof lines. Better for shedding the snow. Probably wasn't necessary. You concede width (obviously) of the floorplan. And you also concede ventilation in the name of shelter.
View attachment 55134
Same A-frame. . but not staked with the corners stretched. I went in 1x stake loop and angled the door in. I've used this once when there was a significant wind shift was expected. I'll be honest. . it was awesome. I was so dry behind that staked flap. But I was also HOT. Very little ventilation.
View attachment 55135
Full Disclosure: I've never used this following pitch with the DST. I'm sure it'd work just as well as other tarps i've used with the same pitch. I also know this: if I'm down to battening down this tight I am no longer enjoying myself. This is no bullsh*t sheltering. If I'm down this tight I'm also likely folding my ground cloth up the side wall of the tarp a little bit on the inside.
View attachment 55136
You mentioned you liked the "Beak". Here you can see the angle of the battened down flaps make at the vertical support at the head of the shelter.
View attachment 55138
Now here's what I do: I always carry 5 stakes and 2x10' 3mm lines. The flying diamond requires 4x anchor points. The modified A-frame: 5 anchors. Secure a single flap: 6 anchors. Both Flaps: 7 anchors. I say again I carry 5 stakes. The night I needed to secure a flap I had to tie off a corner (the reason I carry 2x lengths of line).
The most versatile piece of gear in my pack!
Hope this helps. Anxious to see other pitches!