Whether your floor is dry or not doesn't have much bearing on if your birds have worms or not. Worms can still travel on either dry or wet ground. And grit doesn't have anything to do with parasites, only the processing of food.
I would suggest using Lyme to absorb, or using a straw base that you can change out every week. Ideally you don't want a clay floor, for that very reason. I might suggest to try a dig or drill a drainage hole or trench, not big enough for something to get it to hurt the birds but just to help get the water flowing out of the clay.
Also a good de-wormer will help. That is generally why worms end up in the eggs is because there is an infestation in your bird that has gotten out of hand. Feeding diatom. earth will help maintain the population after a good worming. You can use a chemical de-wormer or you can use ACV, pepper, or garlic in their water and feed for two weeks straight.