Although you should be able with to craft more than 1 rooster/goat/donkey (max of 4 or 10), the crafts prematurely disappear from the garden shed when you finish crafting the donkey. I’ve also posted this in the bug thread.
Not that I really want to expend all this energy for more than one of each especially after a monster hunt but the rooster and goat may be useful crafts for others. The drops while looking fantastic on paper, bear in mind that they are not guaranteed drops. Got roast chicken (black flagged) and silky fur (black flagged) from the rooster and goat respectively last collection.