Correctness of following algorithm for 3-QCNF?
Your code ignores quantification levels.  Formulas prefixed with
$\exists{x_1}\forall{x_2}$ are not supposed to be evaluated the same way as those prefixed with $\forall{x_1}\exists{x_2}$.  Your code treats them the same, moving one existential quantifier ahead of all the other quantifiers in each of your 2-QBF subformulas.