I came up against the same question a few years ago. The published numbers for the weight of baled hay in engineering references are ridiculous at 20pcf. Dry pine is 26 pcf. Those are some balers! I weighed some bales and came up with 5 to 7 pcf. I ended up designing the mow floor for 100 psf, mostly for the tractors and haywagons. We were using recycled timbers hewn on the top side only. We selected the largest ones for use in the two bays with the doors. I also rationalized that as the floor deflects, the hay over the posts does not. If the bales are laid-up in a running bond as in masonry, the posts could theoretically support an inverted pyramid of hay. It could be argued that the weight of of the hay on the joists might not exceed that of a pyramid of hay whoose base is the size of the bay. A similar concept in 2 dimensions is used in designing masonry lintels. Hay is structural in another sense: How many barns have you seen that probably wouldn't survive a winter unless they were stuffed to the gills with hay to prevent them from blowing over? I pass a few like that every day (and few that are empty that should be shored with hay.)
Good luck,
Chris