I would cut the large piece from a template, and then cut "exact" size strips and corner triangles and sew them on.
In fact, I would cut the strips on the bias, so when the unit is complete, all the threads would be perpendicular to each other.
Or - one could cut the large piece from a template, and then sew strips on and then trim to the "exact" size wanted/needed.
Paper piecing would also work -
When my pieces are cut "to size" - and I pinned carefully - things usually line up the way they should.