"How can the third-person requirements of the scientific method be reconciled with the first-person nature of consciousness?"
"Science will find a way"
Admittedly it is optimistic presumption on my part, and may be that science (as a method) will only be part of the ingredient, but it has nothing much to do with science displacing anything, or for that matter EVE having any power to replace/take the place of subjective experience as was stated
here
You could of course provide some examples as to what you understand to be EVE's then together we could look at these and see where they trump subjective experience/opinion/belief.
After that we can ascertain whether trumping means anything much in relation to the subjective.