Unexpected messes after I switched my rabbit’s hay brand

I recently changed the brand of hay I give my lop-eared rabbit, hoping for better quality and freshness. The new hay smells great, and she seems to nibble on it happily, but I've noticed she’s making a bigger mess than usual - hay strewn all over her pen and even scattered outside it. I’ve tried using a covered hay feeder to keep things tidier, but she keeps pulling the hay out and tossing it around anyway. I want to keep her environment clean without stressing her out or limiting her access to the hay she clearly loves. Has anyone else had this happen after switching hay types? How did you manage to keep the mess under control without making your bunny unhappy?