I'm not fitting expert, but it looks like the toe is striking the turf before the heel, dragging the heel forward, leading to the diagonal exit shape you see. Basically, the heel is rotating around the toe a bit? Would expect a slight push as well as a fade shape. Worth checking lie as you may need to go more upright.
Looking at the bottom of your clubs, do you see more wear at toe? Ideal lie, loft and strike pattern should see even wear from toe to heel and on the leading edge.
You say when swinging well, your shape is a draw? One reason could be a slightly more inside downswing path giving rise to a flatter and more level club at impact.
Just some thoughts for consideration. You can ignore if needed!