If the Bayer doesn't work completely, you might consider mixing a few tablespoons of neem, canola or soybean (vegetable oil) with water in a spray bottle (shake it up every few to several sprays) and occasionally spray the soil surface every week or two, perhaps, for a while. Spraying the plant with the same (especially the undersides of the leaves and new growth) should help against mites, too. It may outright kill the mites, but whatever the case, it should make the leaves too sticky for the mites to move much (kind of like a sticky fly strip).
You might also consider giving the soil more light (especially sunlight), but bright light, whatever the case. This should help to reduce mold and fungus generally. If it's warm enough to take the plant outside in the day, you can try that. Just make sure it's not too harsh an environment for your plant and that new pests aren't about to infest your plant.
Air circulation should help. Soil drainage should help.
New soil could eliminate the fungus problem (not the mites), if it's the right kind, and if your environment isn't spreading mold to your soil, but as J. Musser said, it may or may not shock or kill your plant.