Is it possible to perfectly align a stencil?

I haven’t gotten any responses to the question I asked here, so I’ve decided to ask the same question again in its own forum topic, in the hope that the greater visibility that can lead to better odds of someone offering some help.

As I previously stated in the other topic, I’ve been having trouble with trying to align a stencil to the absolute center of the mesh I’m working on, so that the “eye” texture I intend to paint will be perfectly symmetrical on both sides. When I’m working with geometry, I can easily align it to the center by simply setting the XYZ-coordinates to 0, this also applies to things like scaling where you can press the ‘2’ button on the keyboard to expand an object’s size by a factor of 2, giving you precise control over how you can manipulate the geometry. Unfortunately, thus far I haven’t been able to find any equivalent options in regards to positioning the stencil over my model.

There’s also another issue that I brought previously as well. The issue is regarding how the eyes, when applied, look when viewed from different angles.

The eyes look perfectly fine when viewed from the front, and also fairy well when viewed from a sideways angle. The problem occurs when you look at it from a downwards angle, the shape of the eyes become quite distorted, taking on a very angular shape that isn’t desired.

I was wondering if there’s anything can be done without radically altering the shape of the eyes or if I’m going to have to simply avoid positioning the character in ways that make the eyes look so distorted.

As always, any help would be greatly appreciated!

Link to Blend File:

keep your stuff together, don’t spam just because you feel you’re not getting any