Pests, like external parasites (mites/lice), or internal ones (worms)... or external ones like rats (rats do steal eggs by rolling them away... I've seen this).
High humidity and elevated temps can make them overheat and be less comfortable so to say. They rely on evaporative cooling through panting because they can't sweat.
However, with your note about change in diet, that sounds like the key to your egg "problem". Technically, egg laying ration is a balanced diet for efficient egg laying. Eating only formulated feed should produce you steady eggs. Adding supplements, especially ones that throw off the balance in the formulated rations, can and often will disrupt egg laying or reduce it, if they are not getting enough net protein or some other mineral/vitamin. Even if soaking cracked corn allowed for 100% uptake of the 8 or 9% protein that it contains, the feed is likely 14-16% protein. You can't get what isn't there in the first place. If you want to keep feeding soaked grain, I'd make sure that it is no more than 10% of their daily feed intake. If they are eating their eggs, that can be a hard habit to break... so I'd really try hard to rid of the issue. A few shells can easily mean a good number of eggs are missing. They can be real good at eating up the evidence.