what we're looking for is a population who search faster than the natural decay rate

Is this correct? Imagine a least-convenient-genome where every mutation causes instant death (but the mutation rate is low enough that some offspring survive). Then the decay rate is nonzero but the search rate appears to be 0.

My point is that "search" in this context seems to imply seeking out new innovations, not merely maintaining a stable population. The search rate only appears relevant to survival when the environment is changing.

"Rate of search divided by rate of change of environment" might be an interesting metric (where the "environment" obviously includes other populations of replicators who have their own search rates). Possible division-by-zero error if neither the phenotype nor the environment seem to be changing very much.