Basis Conversion for Group with Skinned Mesh(es)?

To preface I’ve referenced the following threads:

Convert from one coordinate system to another?

and

Standard Orientation of the World Coordinate System

But neither seem to work properly for me. I have a group which contains a skeleton and several skinned meshes binded to that skeleton. I need this skeleton to match my standard skeleton I use all the time so that when I apply animation data to it it works as is. After tweaking around with my animation data, I’ve determined that in order for the animation to work, the y and z quaternion values need to be negated.

How can I apply this transformation directly to my group such that the group, skeleton, skinned mesh geometry and all remains intact? (When trying to apply the matrix to the skeleton directly, the model geometry warps due to it being binded).

Below is the matrix I’m applying
[
1, 0, 0, 0,
0, -1, 0, 0,
0, 0, -1, 0,
0, 0, 0, 1
]

Edit:

I am applying the matrix as so:

const threejsAxes = '+X+Y+Z';
const targetAxes = '+X-Y-Z';
const conversionMatrix = new Matrix4();
getBasisTransform(threejsAxes, targetAxes, conversionMatrix);
group.traverse((o) => {
  o.applyMatrix4(conversionMatrix);
});
group.updateMatrixWorld(true);

When inspecting the skeleton, everything looks correct afterwards. However, since the skinnedMesh was binded at that point, the geometry is all jambled up.