i am also working through same challenge. one thing i have started to do recently is to triangulate the inside hidden corner of the box before finalizing the last corner of the outside of the box.

my process has gone to:

1 start with the y

2 draw two planes, usually bottom of the Y, ensuring adequate convergence

3 triangulate the "hidden" inside corner but dont yet draw the hidden lines to it

4 triangulate the top outside corner with the help of the inside hidden corner

hope that makes sense. it has helped me