Another idea in the shower this morning: I can require the existence of computation trees that have some particular branch which itself uses every rule unboundedly many times. This brings things back to a structure that much more strongly resembles the original lemma, namely that this path is "one-dimensional", so I may still be able to coax the graph theory machinery into working. Although if I am forced to think of the rules as being parameterized by one of their inputs, then I wind up with the same infinite explosion of rules. Arg. But, because of the above insight: in the GVCSS construction, I should use max not plus.
Pete and martin (combinator) should be arriving today, and I think nickjong, dr4b, eub, adam, and rehana may have already shown up.