I've made a vertex group on the model of edges I want to displace:
In Vertex Paint mode (Vertex Selection) I selected the vertex group, and then set that full black (Paint > Set Vertex Colors):
Overall, this is doing what I need -- the lines and nice sharp corners marked with green arrows are exactly what I'm going for. The triangular blob-of-black corners marked with red arrows are what I need to be like the green-arrowed corners.
Using this as a displacement map for the seams of a patches effect is the goal -- this shows the green-arrow corners doing what I need, while the red-arrow corners are causing triangular depressions:
Using a Subdivision modifier thickened / rounded all of it, as did assigning a low Weight to the Vertex group and Paint > Vertex Color from Weight:
The pics and blend file attached are an example of the problem, the models this is intended for are larger, with more patches, and a lot more of these corners. Any answer that requires labor-intensive work on each problem corner won't be a workable solution.
Part of the reason I'm using this method (and 3D art in general) is that I have a sheaf of disabilities that make hand-painting difficult for me. Any variation on “Why don't you just paint . . . ?” won't be a workable solution.
Edited to clarify (thanks calambre): The example model, and the models this is intended for, are "good" all-quads topology and should remain so. Any answer that requires changing the topology from all-quads, or in ways that can cause other issues (adding poles that can cause shading artifacts, for example) won't be a workable solution.