interesting question......I too have never experienced anyone who has treatment for exophthalmia due to hyperthyrodism, however treatments are available starting with giving steroids in the early stages.
Now, if the patient is experiencing double vision or other visual problems then to protect the cornea, two procedures come to mind.
a) Lengthening the eyelids to cover more of the conjunctiva. but patient's complain that the cosmetic result is unacceptable and the operation is very rarely, if ever performed.
b) A surgical expansion of the eye socket allowing the eyeball to fit more neatly...another bl00dy awful procedure which goes under the name of the surgeon that originated this operation..called Nafzigger (Google it) and another modification by some Japanese chap Gosha or something (I have just made that chap's name up because ihave forgotten it :-)
That is the best that I can do.........sorry.