This is already how the directional pad mode works on the controller, no? Minus a mode shift listing for each direction. Having to swipe your thumb across the pad while pushing down is really uncomfortable, though. You're grinding on it, which compared to a traditional d-pad tilt, takes a bit more force, and feels uncomfortable. Maybe not in more relaxed games, but in games that require quick directional changes, like Super Meat Boy, it's a tiring motion. At least, from my experience.
Having four switches underneath the pad rather than one gets around this. Tilting is now doable, which would relieve the extra movement needed in the left pad's current d-pad solution. And when it's not in digital mode? Just have all the switches count as a single input. It also shouldn't have a pivot point. I have a Logitech controller with a d-pad that lacks a pivot point, and it's never been a detriment. It would also help in the case that you need to press in the center of the pad for any mode that isn't directional pad.