Try to increase the numerical accuracy to a minimum of 4 decimal places. In your files, you only have 2 (0.01"). I always work with 6 for Numerical Precision and 4 for Angular Precision.
Also, I recommend that you switch to Stick To Edges in the Snap Options and be careful when using Give Guide Snaps Priority. Also, consider using Snap to Endpoint and, in general, not use Snap to Segment, Snap to Perpendicular, or Snap to Intersection, only when necessary.
In both files, I derived the faces, projected them to the work plane, and extruded them with Reshape. Then I had no problem inserting segments at the vertices.
I hope it helps.