Sorry, but I serious doubt a shaft will play differently when one hundredth of an inch of wood is removed from a 13mm shaft. Especially if the shaft already has a pro taper. It may feel better to the player taking into account hand size and such, but that's about it.
Alan
First, where is the balance point on the cue butt with the shaft now? Second, the front of a cue butt is a stress point and you will be weakening that part by creating a cavity. Third cavities can resonate, so again probably not a desirable thing. Just my morning thoughts before coffee.
Alan
I'm assuming you entered 1.125 as your cutter diameter. The Center of your tool needs to be zeroed on the point of your dead center. If you are touching off the cutter to the point of you're dead center, that is where your error lies.
That's why I said most taps. I don't know of a bottoming tap for 3/8X10 or radial, but I suppose one could be custom ground. I prefer the piloted version of those myself. In any case, Happy New Year!