Botrytis Advice Please.

My lilies were all doing wonderful until this past week. We have had rain almost everyday and it's been very humid to the point that it looks like there is steam in the air. Today I noticed all of the lilies have Botrytis, I didn't know until I searched lily disease and the photos and discriptions are a perfect match! Aaargh! Can anyone give me advice on how to handle this? Is it okay to cut spent stems right down to the ground? Can the lilies that haven't bloomed be saved? I read an antifungal spray could help, and I read it will only affect the lillies by not allowing the bulbs to increase this year. I also read I should be sure to remove debris. I sprayed them this evening with neem thinking it was from the darn japanese and asiatic beetles that I keep finding on them, but I was thinking there is no way they could do all that damage that fast! So thank goodness I searched or I wouldn't have known any better and would have just left them to die.
Here is a picture of one before botrytis - taken just four days ago - it has spread like wildfire!
When the sun comes out I will get a picture of the tragedy they are now : (

It's awfully hard to stay on top of botrytis when you get as much rain as we've all had this year. You'll need a fungicide of some sort ~ do you treat anything else in your garden, such as powdery mildew or black spot on roses? That should work. I haven't used Neem myself but there are several products that can be used, like copper sulfate.

You don't need to cut everything down at this point but affected foliage should be removed and discarded in the trash. Leave any good foliage as this will be beneficial for next year. Go ahead and let them bloom if they're able.

Thank you for the help. I do have a product for black spot and mildew so I will try that.