I guess it goes in the middle of the hole. I don't think sliding a piece of hardened steel on wood or brass is going to dull the point, the sharp part doesn't touch anything but leather.
Part of your problem may be that your awl blade is too long for what you are doing. The closer you can keep your hand to your work, it's easier to keep the same angle. Unless you're stitching something really thick, you don't need a long awl, but of course, everybody thinks bigger is better, so small awls are hard to find. I generally like a smaller haft also, for finer work I cut the knob off the end so I can palm the whole thing.
Another problem is our stitching horse jaws are too tall. If the forearm and upper arm formed a ninety degree angle, you could keep exactly the same angle with every stitch and not have to think or worry about it at all and there would be less fatigue all around.
Have fun,
Kevin