Let's see if I can explain how the idea of "good days" is tied to mold avoidance. (And if I succeed, maybe somebody can go explain it to Nancy Klimas.)
"Good days" (at least for some ME/CFS sufferers) are tied to low levels of biotoxin exposures. "Bad days" are tied to high levels of biotoxin exposure.
Biotoxin exposures include toxic mold exposures (mostly inside buildings) and toxic cyanobacteria exposures (mostly outside buildings).
When people get a bigger than usual exposure, they experience a "flare." This may go on for anywhere for a few hours to several days (sometimes even longer).
If people manage to get especially free of this stuff for a while, they experience a "good day." This goes on until the next biotoxin re-exposure.
These things cause biotoxin exposures to be higher:
1) Being inside moldy buildings
2) Being exposed to possessions that have been contaminated by moldy buildings
3) Outside air has a lot of cyanobacteria in it. (This happens more often during certain seasons of the year - often fall - and on cloudy/stormy days.)
If people live in a house with a lot of mold in it, in a country with a lot of cyanobacteria outside, and not much sun, they're unlikely to have many good days. This often happens to people in England, for instance. (People from England tend to report remissions when they go on vacations to Greece, which is why Sarah Myhill advises patients "I'm afraid you'll have to go on holiday" to find out if they have mould problems in their homes.)
What "extreme mold avoidance" does is take advantage of those principles to make every day into a "good day." By not going in bad buildings, not being around moldy possessions, and not being in areas with a lot of cyanobacteria in the air, wellness can be maintained all the time.
This does not mean that mold/cyanobacteria is the cause! Whatever is making us so reactive to these substances that we have to avoid them is the cause.
I believe that the thing that is causing this reactivity is XMRV.
Erik Johnson is part of the original Incline Village cohort (the one used in the WPI XMRV study). He's the person who figured out how to make use of the good day/bad day concept to make every day a good day, and an increasing number of people with classic CC CFS have replicated his success.
So it seems that XMRV doesn't cause the symptoms directly. It sets up the condition for the mold/cyanobacteria to cause the symptoms.
(The herpes family viruses do seem to cause direct cognitive problems, I think. My cognition didn't return until I finished a course of Valcyte, for instance.)
Regarding antioxidants: the way that toxic mold exerts damage to the body is through oxidative stress. Thus, supplements that combat that oxidative stress may be effective at taking the edge off exposures. These can include Vitamin C, melatonin and pycnogenol, amongst others.