You can get the result, but basically one vert at a time so the dragging can be manipulated to the wanted direction. I think Blender gets confused as there are different directions for ever vert when you try to do it like that all at once. Some are slightly left and down some ar slightly right and down, others forward/backward, and combinations of them all.
So, select a vert to slide. GG drag down the edge you want it to go along and check the distance (top left of the window), when it is about where you want it, type in the number being shown as slide distance. I round off for ease. So if the drag is about right and says 0.763935 I type .76. Now you have a number to type for each vert as you repeat the actions, so they all go the same distance.