Importing non-uniform scale joints from Maya

I have a Maya rig for a cartoon character who has non-spherical eyes, achieved using one joint to scale the eye to the desired oblong shape, and 3 joints under it to rotate the eye and eyelids, so that the eye and eyelids will rotate within the non-uniform scale set by the parent joint.

When importing this to UE4, something goes wrong. I’m new to UE4, so excuse me if I use the wrong terms here. From what I can tell, the skeleton I import without animations seems to leave the scale of the eyes at 1-1-1 (and has the eye geometry way outside the eye socket as a result), while in the default pose in Maya, the scale of these joints is set to 0.888.-0.696-0.581. When importing a baked animation for this skeleton, it makes a half-hearted attempt at scaling the joints. In the model viewer, the scale values of these joints are are correct non-uniform value, but the scale is somehow wrong. The eyes are spherical, but smaller instead.

Tampering with the scale in either the skeleton import or animation import results in the eyes and eyelids going completely out of sync, so that doesn’t seem to be an option.