Jason, Overall, Orientals are more susceptible to botrytis than Asiatics. Trumpets are thought to be the least susceptible. Some individual cultivars within these groups are more resistant to botrytis than others, too. Botrytis just doesn't affect lilies as you called it 'lily botrytis' above but can attack virtually any living green leaf plant on the planet. It plays an important role in the decomposition process and as such is ever-present everywhere. So, we live with it and control it and by being proactive in selecting what we plant, we can still have a beautiful mixed garden.
To be frank with you, I don't see the need to dig up your potted bulbs every year as a proactive means of controlling botrytis or anything else, for that matter. Each time you do that, the bulbs go through what is called 'transplant shock'. As far as 'risks vs. rewards', it can do more damage than good by lowering the bulbs overall resistance to, not only botrytis, but other soil borne pathogens that can cause bulb rot, etc.
I assume the reason you're digging and replanting every year is so you can change up the color scheme from year to year. You can still do that but I wanted you to understand what the risks vs. rewards were. Try adding a little powdered fungicide to your soil mix the next time you pot up. Give the Oriental types as much space in the pot as possible to allow for as much air circulation as you can get. Spray mature plants in early morning with a fungicide every two weeks during humid weather above 55'F or after every rain. Try and search out botrytis resistant cultivars (plant name) to use by asking questions. It can be done!!!