Hi Caroline,
I am sorry you are having problems. Unfortunately the quality of orchid bark is variable and it is seldom sterile. For that reason I solely use coarse-grade coconut/coir for Cattleyas and Phals. Repotting is stressful to orchids and sometimes they quickly succumb to bacteria/fungi in the new growing media even if the media looks clean and fresh. If you can break up a piece of the bark between your fingers it is probably decaying. Pouring boiling water over the bark would not be enough to kill spores. You are absolutely right to try and remove all the old moss from around the roots. Moss rots after about a year and needs to be changed. New Zealand Sphagnum moss is best but it is expensive and hard to obtain even online. Cattleyas ideally should only be grown in coarse bark/coir with little or no moss as they must have excellent drainage and air around the roots.
Also it is quite natural to find dead roots when repotting orchids especially Cattleyas providing they are attached to old bulbs. New shoots should have healthy the new roots. Always remove all dead roots at repotting. Personally I feel your orchid media must also be be too wet which has encouraged the mold. If possible I would repot into fresh media obtained from a different source (NEVER use Westland orchid compost, it is dreadful in my experience). Very importantly make sure you do not overpot which could also be contributing to your issue. You could add polystyrene foam chunks as a space filler if you have only a large sized pot. If you have to stick with the current compost then make sure to allow drying out before rewatering the mold should not like that and provide plenty of ventilation on the summer days.
Perhaps other members can make suggestions? I have not used anti-fungicides. Best of luck and let everyone know what the long term outcome is for your plants.