Here is an article for you to read all about roundworms.
Dog Roundworms (Ascarids, Toxascaris leonina, Toxocara canis)
They basically state the only way to really get rid of roundworm eggs from your yard is to remove and replace the soil with new soil...in the depth of about 8-12 inches. Bleach will not kill the eggs as you already know but will remove the sticky outer layer to make them easier to remove. I wonder if Diatomaceous earth would kill the eggs after the sticky outer layer is removed? Many people use Diatomaceous earth to control flea populations in their yard.
Keep in mind as well that an extremely healthy animal is not a good host for parasites and will normally expel them on their own.