When you jog a leader SW puts a section of the leader in the original position before the jog, so that's why your jog doesn't start right at the gauge point.
Ideally you'd be able to just drag the jog all the way left to eliminate that section but apparently SW won't let you do that. There is some minimum length for that section, and after some experimentation I discovered the minimum length is equal to the extension line gap set in the document properties.
One option would be to set that gap to .0001 or something tiny and then you could drag the jog all the way back, but then that would reduce the leader gap on all of the other dimensions on the drawing, so you probably don't want to do that. And as far as I can tell you can't set a custom gap for a single dimension.
Another option is before you put in the jog drag the end of the leader across to before the gauge point, then add the jog and drag the jog so that it points to the gauge point. You can't drag the end of the leader while there is a jog in it, so that's why you'd have to do that before the jog. But since the part edge is tapered then you'd have a small leader segment sticking into the part, which may or may not be noticeable. Here's an exaggerated image to show what I mean.
The only other thing I can think of is you could manually draw the jog, then dimension to the outside points on the jog lines, then override the dimension with the correct value. But then the dimension isn't linked to the model.