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It works, and I think Effie is a very natural nn for Stephanie because the main accented syllable in "Stephanie" is "Eff". Steph / Stephie / Stevie makes sense, and Fannie makes a little sense but wouldn't be 'natural' unless the name was pronounced ste-FANN-ee. But Effie is just as natural as Steph IMO.
As long as you don't mind having 2 nicknames (your family will probably stick to Stevie, for a while anyway), go for it.