I don't think that you only have a fungus problem. The leaves look old and tired even though they are at the ends of twigs where one would expect new leaves to be looking like new. They look like old interior leaves. Is the plant putting out new growth on a regular basis? How old are these leaves? They look undernourished or as though they are growing in a pot with low fertility, possibily due to a low population of mycorrhiza. I don't like peat moss because it alternately stays wet too long or when dry is hard to wet out again. I use composted wood chips instead, but not many others do. Woodchips contain an army of mycrobes that readily convert N, P, K, & micro-nutrients that you add as ferilizer into food for plants. You may consider top dressing with composted leaves, or leaves that have been rotting in a pile someplace if you do not have access to a compost source. That would suppliment the microbe population quickly without repotting. Choose leaves NOT from the Fig family so you don't introduce a natural pathogen, too.