How about a thorough cleaning of the underside with a soap (or saddle soap) using a stiff bristle brush. If that does not solve the problem, how about a minimalist treatment with a fungicide (on the underside only)?

The mold on the outside can be cleaned with saddle soap and a will remain clean by riding the bike, so no fungicide will ever be needed on the outside.

Re-treat both sides with Proofide when done.