It fixes the worst problem, which is the well-definedness of the interior product, since it defines the product explicitly on the standard basis rather than through a bunch of not-obviously-consistent axioms. It is too basis-dependent for my tastes (it should depend on the symmetric bilinear form, not on the basis). As for the sign conventions, I think they're ultimately matters of taste, and while I agree with you about the inner/scalar product, I disagree about the derivation-ness of a contraction (I like it to satisfy the Koszul sign rule, which allows signs to be inserted only when some factors move past each other).

My ideal approach is along the lines of Chevalley's "The Algebraic Theory of Spinors and Clifford Algebras", Chapter III, but he doesn't get to much geometric algebra.