Conclusions: While supplementation with "classical" antioxidants such as ROS-scavengers has many limitations, increasing the intake of polyphenol-rich foods seems to be a promising novel therapeutic strategy to reduce the deleterious effects of increased adrenergic tone, particularly in essential hypertension.
This supports that study on vitamin E in diabetics.
Conclusions: Chronic vitamin E administration improves the ratio of cardiac sympathetic to parasympathetic tone in patients with type 2 diabetes. Such an effect might be mediated by a decline in oxidative stress.
This is plausibly the reason why antioxidants enhance sleep. Though it is likely that there are other mechanisms as well, such as reduced neuroinflammation. Come to think of it, given that ME/CFS appears to be caused by high sympathetic tone during sleep, antioxidants are the perfect treatment. Antioxidants are proven in placebo-controlled trials to help with sleep in healthy subjects and insomniacs alike. I doubt that antioxidants can cure ME/CFS, but I'm confident they will help.