If you can’t buy the hay off the field, I imagine they are using it to seed other fields with a hay meadow flora. So the last thing they want is for it to be “improved” by modern grass seeds!
If it’s a hay meadow for conserving old flower species, then frankly they will not want you putting anything extra into the sheep that you graze there. Increased inputs mean increased outputs, and they will expressly not want fertilisers, natural or otherwise, on there.
So graze it August to the end of October, take the sheep off when the grass hasn’t enough nutrition in it for them, and bring them back for a month in spring if the spring grass comes early enough. Anything else isn’t conservation grazing, it’s farming ;p