Update.
Monday morning the animal rescue people arrived along with a fish and wildlife officer. The bird was still hanging in there, was taken to a "bird hospital" of some sort, and as of today is doing fine and will recover.
What I thought was a wound from another bird actually turned out to be a gunshot wound. The animal officer told us that three other Ospreys were all either killed or wounded over the Easter weekend. One, shot with an arrow, is dead. The other two will recover. It turns out that not to far away at a local pay-to-fish pond the birds were helping themselves to some very tasty trout. From what the animal officer told us the pond owner is currently being investigated, probably charged by now, with the shootings.