Turns out I was wrong about the scaling stuff. You can actually scale using the snapping tool (to vertex), using some helper vertices or other models that may be in the scene. And it works quite well. Somehow I had the idea that it wouldn’t work, perhaps this comes from the times of blender 2.4x where sometimes things messed up, and maybe I didn’t try it out again in 2.5x+.
Anyway, I tried that and it worked wonderfully. It requires just a little bit more work than shrinkwrap and shear, but not really so much that makes it tedious.
After I made the quarter-dome I created a separate vertex, snapped it to grid (selection to grid), then snapped the model’s corner to that vertex. That aligned that corner to the grid just fine. I then placed the cursor at that corner and created another helper vertex exactly 6 BUs away from the cursor, horizontally, and scaled the whole geometry so that I snapped the second corner to the second helper vertex (sometimes this doesn’t work if the vertex is too far from the geometry you’re scaling, in that case you can scale it to reduce their distance and then scale again and snap should work).
Then all that was left was the converging point (the V-shape), I placed another helper vertex at the correct spot, aligned to the grid, placed the cursor at one of the vertices on the side opposite to the V-shape’s point (anywhere will do, as long as it’s on that side) and the V-shape scaled perfectly away from the cursor and snapped to the helper vertex.
So that method is actually viable even without the shear tool, after all.