Well, I would dispute the claim that Cheney changes his mind every 5 minutes. Once he started using echocardiography, he started testing how various supplements affect energy production among his CFS patients during their echocardiograms. Some supplements turned out to have a negative effect on echo paramaters.
I have been his patient for about 10 years and he was never really a big proponent to me of using a lot of antioxidants. According to his nurse practitioner a few years ago, some of his patients use very few supplements and some use a shotgun approach and try everything that seems promising that they read about on the web. In the past, he looked over the list of supplements I was taking during my office visit and at times would recommend that I stop taking something that I had read about elsewhere as promising. For example, he recommended I stop taking NT Factor.
But, getting to your question: he has tested numerous antioxidants and supplements on the echocardiogram and finds that a few have positive properties. In general, they tend to be from companies that seem to focus on using "whole foods" sources. So he recommends patients take Mediherb's Vitanox and Mediherb's Hawthorn and Innate Response's Adrenal Response, since they evoke positive responses on the echo. He also likes the multivitamin from Standard Process (if you can tolerate gluten). He recommends patients get their Omega 3-6-9s from organic olive oil, which tests positive on the echo. Fish oils do not test positive -- I think he suspects they become rancid much too easily. Similarly, he doesn't like vitamin E because of rancidity issues. In keeping with the whole foods approach, he recommends juicing of green vegetables and eating organic dark chocolate (at least 70% chocolate) and/or organic cacao nibs in small amounts. For gut function, he now recommends patients take goat's milk kefir as a primary therapy. Dietary modification is also considered to be very important. He recommends patients eat mostly vegetables, some proteins, and limit starches. He recommends avoiding sucrose and high fructose corn syrup and almost all sweet citrus/tropical fruits.
His real focus is on using cell signalling factors and stem cells to treat patients. Obviously, these treatments seem "way out there" but I have found that they work to a surprising degree. As he now thinks these treatments are far more helpful than supplements, he doesn't spend a whole lot of time recommending supplements. My guess is that he would prefer his patients use all the cell signalling factors and go for the stem cell treatments and take no supplements, rather than the other way around.