Good point. I take the claim that a sentence S is meaningless as equivalent to the claim that S has no truth-conditions. Let A be any schema for the conditions on which a sentence has truth-conditions, so that for each English sentence S, A(S) is true iff S is meaningful/has truth-conditions. Let S be the sentence ~A(S). Then S has truth-conditions iff A(S) iff ~~A(S) iff ~S. Contradiction. Nowhere was it assumed that the contradictory sentence was meaningful.
When you state A(S) iff ~S, you are formally substituting S for ~A(S), but the meaning of "A(S) iff ~S" is "the set of truth-conditions for ~~A(S) is the same as the set of truth-conditions for ~S". But this assumes that there exists a set of truth-conditions for ~S, which assumes that there exists a set of truth-conditions for S, i.e. that S is meaningful, by your definition.
Graham Priest discusses The Liar's Paradox for a NY Times blog. It seems that one way of solving the Liar's Paradox is defining dialethei, a true contradiction. Less Wrong, can you do what modern philosophers have failed to do and solve or successfully dissolve the Liar's Paradox? This doesn't seem nearly as hard as solving free will.
This post is a practice problem for what may become a sequence on unsolved problems in philosophy.