In the meantime, perhaps a visual aid might suffice? Since the Ctrl+shift drag constraint feature works with the Fill Tool, as well, if we load a pattern into the Fill tool we can guide which direction the fill is laid out. So by loading an image of a single line as a pattern, we can lay out a directional aid on a new layer. Then, by holding ctrl + Shift to make our lines, we can ensure the lines are correct, as they should fall parallel to the guides. Below, you'll see an example experiment I made (the pattern fill lines are the red lines), along with the image I created as my line pattern for the fill tool.
Here's the image for the Fill tool pattern:
Nothing is easy to the unwilling.