With no anecdotal evidence for now, I'm going to do Theorymon and guess.
"Simple now doubles the number of stages in a stat change rather than doubling the effectiveness of each boost...
"The move Simple Beam can change the target Pokémon's Ability to Simple. Pokémon that receive Simple will not have pre-existing stat changes doubled."
"The boost removal is now shown as stat drops."
So theoretically you should have +3 Def and +3 S.Def after 3x Stockpile, after getting hit by Simple Beam, using Spit Up/Swallow will leave it at -3 Def and -3 S.Def
(I'm not gonna talk about Gen IV and lower, it gets weird from there.)