Hmm, not sure what core L/D would do, but I can see how tweaking the core shape might also help eliminate the tail-off. Maybe instead of a simple circular port, a teardrop with the point towards the center of the grain would eliminate some of the slivers (though it would also make it a faster burn).
Fortunately, openMotor can help answer questions like this, because rather than using closed-form equations for calculating regression, it calculates the distance transform of the core geometry and then finds level-set contours on it to determine the surface area of the grain at any regression depth. This means that in addition to the preset geometries available in other software, it also allows you to load in a custom port geometry from a DXF file and simulate it just as easily.