Adding a small disc of white sponge, cut from a makeup applier/remover sponge, cut the response time in about half. That is pretty good, but not as good as I hoped.
In addition I assembled a unit using Tyvek Priority Mail envelope material as a membrane approximately as shown in this sketch:

This one had the same size cavity and the same size sponge in it with the same amount of KH water and indicator reagent. It responded the same as the other one, so I think Priority Mail envelop Tyvek is a good membrane material, and again, the results are pretty good, if not as good as I hoped.
This one is very easy to make - it took me about an hour start to finish.