Mark, did not find a Bohlich in Zella, but there may have been just a change of spelling. In common German Bohlich and Bohlig are spoken just the same. There are 7 Bohlig gunmakers mentioned in Zella, Mehlis with one moved to Berlin. These may have been your relatives. Valentin Ernst Bohlig, mentione 1888. Friedrich Bohlig, Hammerroedchen 14, Mehlis, mentioned 1897-98. Albert Bohlig, Kuhstirn 20, m.1898. Theodor Bohlig, Meininger Str.320, Mehlis,1897. Bohlig & Esch, Malzhügel 1,Zella-Mehlis, 1899-post 1935. Adolf Bohlig, Zella-Mehlis, Kleintiegel 20, shop in Berlin, Stubenrauchstr.6, since 1900. succeeded by Fritz B. (son?), 1900-1942.
But your rifle was not proofed at the Mehlis proof house, as from 1911 on M. not only stamped the bore diameter in mm, but also always added the proof date, month/year, and a ledger number for that month. So it is unlikely that any part of your rifle ever saw Z-M.
IMHO now, the service powder charges for the 8x57I may be used for dating the rifles: 1888-1901 = 2.75g, 1901-1910 = 2.67g, 1910 on = 2.45g. Your rifle was probably inadvertedly with the "old" charge, then corrected to the "new" standard sevice charge. Powders and charges changed, but ballistics and proof load remained the same.
I too have not yet seen claw mounts like your's, but similar mounts with a wide spacing of the front claws and an offset rear base are sometimes seen on regulation Gew98 Scharfschützengewehre. Those were still the formative years of scope mounting. All mounts were hand made by many individual gunsmithes. As it is known that Collath mounted many scopes in WW1, it may be an early "Collath" mount. It is quite hopeless trying to find a scope with tops that fit your bases exactly, so I would fit some modern bases to your rifle, if possible, using the existing cuts and holes.