It's easy to break an approximative definition by applying it to a situation where distinctions between orders of error are important. So any such definition, strictly speaking, has to be considered a sort of analogy or metaphor that may not always be applicable to every context.

Strictly speaking, as you know, "E screens F off from A" means P(A|E&F) = P(A|E&~F). So it seems reasonable to say "E approximately screens F off from A" if |P(A|E&F) - P(A|E&~F)| is small. However, what "small" means is context-dependent. When, above, I declined to apply this terminology to E and F, it was because I was mentally comparing |P(A|E&F) - P(A|E&~F)| to |P(A|E) - P(A|E&F)|, rather than to |P(A|F) - P(A|E&F)|. The latter, of course, is much larger. So I don't suppose I can really stop you from applying the approximative definition of "screening off" in this situation if what you're interested in is P(A|F) vs P(A|E&F) (a large downward jump) rather than P(A|E) vs P(A|E&F) (a small upward jump).