THIS IS NOW RESOLVED. See comment below.

Background: I've created sets of male and female characters in CC2 using head meshes from Reallusion's "Universal 3D head" / Realistic Human 100 pack. I exported sets of male and female characters from iClone using an specific male and female model, and imported them into Unreal 4.19, using the UE4 skeleton.

Problem: In Unreal, each female animation plays great on all the female characters. However, with the male animations, they look great on the character with which they were exported from iClone, but when the same animations are applied to another male character in Unreal, the eyes are usually not in the correct place (for some characters the eyes are in the correct place, but for most characters the eyes are either sunken or bugging or too high or low).
This is a problem because each animation should work correctly on all characters using the same skeleton - as they do for the female animations.
It is also very strange because:
The male characters look perfect in the Skeletal Mesh window in Unreal; it's only when you play animations that the eyes become misaligned
As I mentioned, the female characters don't have this problem; all anims work perfectly with all my other female models.

What I've discovered: I've done extensive troubleshooting / isolation testing and believe the source of the problem is with the male RLHead meshes. What I noticed is that animations imported using one head mesh won't be compatible with other head meshes UNLESS the eyes of those characters appear in exactly the same place in CC. The only workaround I've found is to only use head models that have their eyes in the exact same place, which limits you to a small handful of male heads, of a total of about 50.

Question: Does anyone know why this is happening or have a better workaround?

Things I've tried already, which didn't work:
1. I exported the same animations from iClone using a different character. Unfortunately anims imported with Character A caused Character B to have popping eyes, while the same anims imported with Character B caused Character A to have sunken eyes.
2. I tried tweaking all the iClone export settings (including deleting unused morphs), but nothing I did made any difference.
3. I tried exporting the anims from iClone using the default male character model, but when playing those anims the eyes on all the other RLHead models didn't play correctly.
4. I tried exporting anims from different sources (iClone, marketplace, etc) but the problems persist so it's not the animations' fault.
5. I tried the whole process using a new Skeleton in Unreal and the same problem occurred.
6. I tried re-making the models from scratch and exporting / importing them one at a time, and the same thing occurred.

I'd be grateful if anyone could help with this! :-)