I was able to clarify a gallon of heavily re-brewed EIS
with about 2 ml of h2o2 in 3% solution. I let the batch
peroxidize overnight, after letting the final re-brewing
of the EIS stabilize for a day.

Maybe the h2o2 is acting as a catalyst in splitting weak
planes in the crystal lattice of the particulate fraction. If
so, the important quantity may be the product of h2o2
concentration multiplied by the runtime, moreso than either
factor separately. 

Though I have no evidence for it, I like to think of the
h2o2 as splitting crystals, like a knife blade used to
split mica into thinner and thinner crystalline sheets;
time is a factor. Maybe the process could be made
visible by observing the changes in TE at two different
wavelengths, using both red and green laser pointers.
Just a passing thought.

Matthew