I would stop the egg for a couple of days and see if the droppings return to normal, if he is eating more veggies than usual that could account for the wetness. Does he eat pellets, in birds that eat pellets the droppings can have a brownish cast to them. Do you have an avian vet? If so you may want to take in a fresh dropping and have them test for bacteria, fungal infection etc. that way you can be sure nothing is out of order.
I wouldn’t feed egg every day, even when molting- that’s a lot of protein. Maybe every two-three days? Veggies are fine, it’s just the extra water and green veggies that’s making his poop greener and watery I think.