Any recommendations on joists for weight bearing?
68.57 Pounds per square foot if evenly distributed - call it 70 (or 75) and pull up a calculator (or drop by your lumberyard and have them run it on their I-joist software, which might well be the most affordable solution.) Or hire an engineer.

Underbuilt haylofts do have a tendency to demonstrate that they are underbuilt; so don't underbuild it.