Input from Rick Snow via a post on the Toned Proof Indian Cent Collectors site:

We can thank Dealers from the 1870’s and 1880’s for these toners. David Proskey, A.M. Smith and others bought the remainders of the cent, three cent and five cent Proofs from the Mint at face value at the end of each year. They held them in envelopes that toned them until they died. They were distributed mostly in the 1930’s. By then they had acquired incredible toning. They started acquiring them in 1877 and continued until 1916. Some dates were vastly overproduced, like 1885, and they had huge hoards of them. Other dates, like pre-1877 were not saved as much.

Thanks Rick