I use hydrogen peroxide for thrush but you have to be very careful with this so probably not recommended for the novice. Betadine or Thrush Buster is probably a safer bet. I can't see how MTG (mineral oil and sulphur) could combat thrush, so I think you should be resigned to having something that deals with each separate condition, as they are not related bacterium in these separate conditions.
Old fashioned Lysol concentrate. 1 part Lysol, 10 parts water. Soak 15 minutes, 3X a week to kill the critters.
In between, pick & brush out well... copiously spray with Athlete's Foot Powder Spray
I haven't heard of that soaking method. Have you heard about soaking with salt water? Someone recommended that to me after explaining that her horses' feet always look amazing after a trip to the beach.
I've also heard great things about No Thrush powder. I've just started using it and its really easy to apply.
My blog about buying back my first horse and regaining skills lost after 6 years of not riding.