This is a very nice approach. Unfortunately, Piantadosi's pairing function does not work for acyclic grammars (i.e., finite CFLs). We found a variant that handles enumerating all trees of a certain width from an arbitrary CFG, i.e., L(G) ∩ Σ^n, or whose language is finite [1]:

[1]: https://github.com/breandan/galoisenne/blob/master/latex/laf...