If they need to be 'lifelike' and crispy, the best way to store them is on the plant in the ground, honestly (i.e. do not pick til needed, and plant successions so there will always be some new stuff coming on). In the fridge crisper, with the plant picked whole and dirty roots cut off and egregious dirt washed off leaves, then lightly spun/shaken dry and put in a SLIGHTLY VENTILATED hard container, they will last for a week or two, maybe a bit more if you are careful in cleaning/storing and not too picky about what constitutes 'safe for animal consumption'.
Unfortunately any type of freezing, canning, anything like that will result in a mushy blob (have you ever bought frozen spinach or collards?) that still has most of the nutrients but you'd have to see whether the animals were willing to eat it. Similarly, proper drying retains a reasonable degree of nutritional content but gives you a very different product.
Good luck,
Pat