The dreaded white fungus/mold -- how best to manage

[cythaenopsis]

When I unpotted my phal to check on the roots about a month ago, I had noticed some white fungus forming in some of the moss. I threw that portion out and reused the moss, because I didn't have any fresh moss on hand. What a mistake! Of course, fungus/mold can exist unseen to the naked eye and some of it continued on in the moss.

Here's a shot of the plant when it was blooming earlier this year:


As you can see in my case, I have a "double phal"--basically two plants that came in one pot. The roots were heavily intertwined, so I had decided to leave them as-is. However, one of the plants started showing signs of some suffering. The bottom leaves began to wither. Out of curiosity, I pulled out the top layer of moss to find white fungus thriving underneath again. Darn it! Also, many of the roots appeared beige in color. Fortunately there are still some green roots, so I think the phals will survive if I handle them right.

This time I decided to separate the two plants... and it wasn't as hard as I'd originally thought. They were strongly intertwined, but with light wriggling over the course of a few minutes, I was able to pull them apart. I'm going to pot them separately now (I have plenty of fresh moss on hand). The larger phal had no signs of the fungus, but the smaller one showed some fungus on the roots.

Before repotting, is there anything I should do to help eradicate any traces of the fungus? I saw someone say they gave their plant a Listerine rinse! Is that really safe to do?