If you need the eye mesh for the vanilla character creation you can unpack it from the Oblivion bsa, into the correct file folders, which you can make yourself if they are not there by right clicking in the appropriate directory and adding a new file, and then edit your race in the CS. This will make it compatible with the vampire eyes, but incompatible with the race's current eye selection most likely. The reason the eyes bug out is because there are two different meshes for each eye with some custom races. I would advise just downloading a race pack that used one eye mesh. Xenius has some very nice characters that are quite popular, and the eye bug is non existant with them I believe. There are many others, but that one comes to mind.
And discussing this mod is a little "taboo" but all the previous issues that caused it to be band have since been resolved so far as I know. You would probably get better support on the main site however
Hope I answered your question.