Mirror object diagonally (or Symmetry about origin), i.e. excusively in X+Y I'm trying to mirror an object like this (see picture) such that the mirrored object behaves exactly like it would using the Mirror Modifier - that is, mirrored transforms and mesh. Currently I have achieved this using drivers and linking mesh data. But can it be done by not using drivers - either by modifying the Mirror Modifier itself, or creating a custom modifier, or by linking a modified source object data, or any other method? 

I'm really grasping at straws because I have no idea about the directions this can go in.

PS: Note that using the array modifier with an object offset is no good since it needs the transforms to be applied.

PPS: You can suggest an Add-on if you know any.
Point Reflection.
As pointed out by @RobinBetts can achieve point reflection by using the array modifier, with offset object and the offset objects scale inverted.

In this case have constrained the offset empty's location to the inverse of the original.
Rotate the Mirror Object.
If the object already has symmetry in X &amp; Y

The mirror object set via the modifier acts like the mirror plane. Rotating the object, rotates the reflection.
In example above, mirroring in $X$ axis, which is normal to the mirror plane, and at the location of the empty.  Any 3d plane can be defined by a point in space, and the normal vector to the plane
Similarly could mirror in $Y$ and rotate empty 45 to achieve same result.