keeperofthehearth, I'm sure you are right. The ultimate solution is to have a separate pen, which I do plan to build once I'm not being distracted by unseasonable snowstorms and unplanned sheep escapes....
I do keep the food dish in the pen filled, plus scatter corn and oats around the pen. I feed hard-boiled eggs as snacks and toss it to different corners of the pen so the 'scovies and the low ranking hens can get some. I throw some grass into the pen every day and today I picked some clover as well and threw a bunch into each poultry pen and boy does everybody prefer THAT to plain old grass. The Muscovies do seem to be getting their chance at the greens pretty well.