I believe the Orphan Roll might be found at: The University of Tulsa The Grant Foreman Room at the Muskogee Public Library The Genealogy Library in Tulsa, OK The Talbot Museum in Colcord, OK.
In addition, the Talbot Museum in Colcord publishes a quarterly periodical, "The Goingsnake Messenger"
I believe this roll has been published in that periodical in the past. In addition, Dr.James McCullagh of the U. of No. Iowa published an article that was featured in four successive issues of the Goingsnake Messenger in 2004 that listed the deaths of children in the Cherokee Nation during this time frame. Some orphans were also listed in that article.
The 1880 Orphan Rolls are preserved on microfilm. You would want to inquire at the above mentioned archives about the availability of this rolls of microfilm and perhaps make an appointment for usage of the microfilm viewers.
These viewers are almost always in use, so making an appointment might save you some time.