You might also attach some raffia to the bale to make it have more dimension. It can be found in both natural and synthetic materials. I have made bales for a ground row before with hay. I base painted and textured the boxes first then sprayed it down with spray adhesive covered with hay and let it dry. Once you have that dry let the excess fall off. I think you could have a similar effect with the raffia.

If it's the actual hay someone is allergic to, then there's really nothing you can do but use some other material. However, if it's the dust, mites, and other debris that exude from the hay, perhaps spraying them with polyurethane would help keep the dander down.

Due to fire code regulations many props artistans build plywood boxes and cover them with bar sipp straws and drinking straws then paint them to get the needed effect. It worked on Hee Haw and see how many straw sets they had.