Well that sure looks like the rifle.
Breezed thru the patent info and appears the lever, lock, belt, ect. was the purpose of the patent. Didn't see mention of cooling.
Peter Sheckler was listed in 1895 census as a gunsmith in Stockton, Kansas.
He died that year also.
Alexander Peterson is listed in 1910 in New Haven as oiler at gunshop.
His son, Alex Peterson Jr. is listed in Military Record 1917 as machinist at WRA.
Not sure who Mr. & Mrs. Thomas Cain were. Found a "Thomas Cain" in Worcester, Mass in 1898 listed as Baker. Not sure if same one.
The limited info found points toward an experimental rifle by Sheckler of the approximate time period.
Alex Peterson begins to potentially connect dots, to New Haven where Marlin was located.
Mrs. Cain may have been Peterson's nephew as she says, but haven't seen the linkage yet.
Regardless, Don should snarf it up, figger it out and report back.