I'm no expert, but i have seen many repro issues in chickens and I do believe that your hen is well past the non-surgical solutions. As for vitamin e, it's probably okay to give unless it's one of them fat soluble types like vitamin d. Like most vitamins, e comes in different strengths, so that is something to research. Send FBC a PM and ask him how many units (IU) he suggests. If it's an oil, giving it with a syringe is risky due to the risk of aspiration and lipoid pneumonia, but no need to tube, you could just give gel caps instead. 
Hope that helps,
Kathy

Hope that helps,
Kathy