It seems to me that there are 2 things to consider: Making more available than they can eat, and providing something that the rabbit does not consider food.
I have 2 holders for grass and hay, one for short or tangled commercial hay and one for long pieces. Last summer I fed fresh grass and tried to keep a good supply. The rabbits would eat from the holder and a bit from what they pulled onto the cage floor but it would build up on the floor while they ask for more. As fresh grass became scarce and there were many brown tips, I would provide some on the tiled kitchen floor and every green bit would be eaten. I have just finished reintroducing fresh grass and when I provide less than what is wanted, whether on the kitchen floor or in the holder, nearly all of the green is eaten. Over the winter I fed commercial hay, some I made, and some silage I made along with a measured (limited) amount of commercial pellets. All of mine was completely eaten but a substantial part of the purchased hay was not. I would delay adding more hay to get them to clean up what they pulled onto the ground. Most would be eaten without complaint but then they would become agitated, hunting vigorously through the house for bits of food and begging vigorously from me while leaving much. (This was not accompanied by weight loss, so maybe they would have eaten more if I persisted.) I tried to see the difference between what they eat and what they reject but I can’t. To me it smells and looks good and I see them eating what looks like the same thing. Looking for mold using fluorescence from 366 nm illumination, I see no difference between the new and rejected hay. As to my hay, it was cut in mid summer from a open field and dried at room temperature with continuously flowing air to a equilibrium relative humidity of 37% then put into a plastic bag which is kept sealed.
