The reduction in worm load could have been coincidental in such a study. Burdens wax and wane based on the season and the load in the environment. I run a LOT of fecal samples on various critters and I could tell you a lot about seasonality and even temperature effects on parasites. 
 
the only way to truly know if your dewormer is doing it’s job is to do fecal examinations prior to treatment, and again after whatever life cycle timeline is for the parasite you’re treating. (Usually for cattle and small ruminants, we check them 3-4 weeks following treatment, to give an example.)
DE is entirely ineffective (for anything) once it is wet. Once it gets into the chicken it’s useless. It is a desiccant. It draws in moisture. I have used it as a layer on top of my feed bag liner prior to putting fresh bedding down, but only to soak up some excess moisture. If I have parasites, I use an appropriate treatment for them.
I have people telling me all the time that they give DE to their calves to prevent worms. What they don’t understand/realize is that the premise of giving the calves DE is to distract them from munching on and licking the things that they would be obtaining oocysts from. So yes, in a roundabout way, the DE is helping with the worm burden, but only by the fact that they are spending their time playing around in it rather than licking the manure off the walls.
As for withdrawal times. If you are using the eggs for your own consumption, and are aware of the risks (if any) involved with ingesting possible residues, have at it. I eat the eggs from my birds after dosing with certain drugs. No problem. 
If you are selling or giving away eggs, you have a moral obligation to ensure the safety of those you are giving those eggs to, or at the very least give them the ability to choose the amount of risk they’re willing to take. If you’re giving eggs to friends or family, give them the heads up and allow them to make their own decision.
One other point on what to do with discard eggs. It was mentioned to incubate the eggs with possible residues. In most cases this probably will not cause any issues. In others, depending on the drug, it may increase your risk of deformities or other problems with the resulting hatchlings. I’ll have to go looking and see if I can find any information on Valbazen in poultry specifically, but that particular medication does have detrimental effects on cow and small ruminant fetuses depending on gestational age. 

 I’m not sure if there are any documented issues for poultry, but something worth thinking about.