I can't find any way around the blinking. The part added to bone will always be slightly larger than than the original model. This means even if you reassign the open eyes texture to this new part it won't blink. AABA is the only one that will blink. I've tried more than a few work arounds and it seems the only way to make the blinking look right is to resize the head on the Y axis to be 99 instead of 100.
Now this does mean his head will shrink ever so slightly in one direction, but I couldn't notice it except on the back of his head...staring very close up and with Cloud facing left. Also, I'm sure NCS knows how to fix the transparency issue using Image2Tex, so that's no problem.
However, I would suggest looking into the c_eye2.tex file replacement. This will eliminate the need for a second head on many models (saving file size), I'm just not sure exactly why the head still blinks slightly using this method... the switch should be instantaneous. If the texture were smaller size it could possibly remedy the blink, but I'm not positive. Test it yourselves and let me know what you think. I'll be checking the smaller texture size to see if that helps.
EDIT
And another discovery, after saving the head change to 99, reopen the model and change it to 101 on the y axis. It will now be the same size as the open eyes model, but won't flicker during blinking.
EDIT2
Nope, reducing file size didn't work. I went from 12mb to 768kb on the textures and it still flashes. So the above solution is the only way to make blinking work correctly that I can find. No need for me to upload the changed model since NCS hasn't quite finished everything and the solution is a very quick fix.