Kevin: I believe the load for the 89 Schmidt Rubin is a lower pressure loading than the current 7.5s are but do not have any data - hold that thought. My Military Rifle Cartridges of the World tells us the cartridge, original to the 1889 model, used a 213 gn paper patched bullet of .299 diameter at 1970'/sec, and was followed by a 190 gn bullet for the model 90/03.
In 1911 they developed the 174 gn boattail bullet of .308 inch diameter which functioned at about a 45.5k psi range while the cartridge for your 89 model was in the 37k psi range.
Your rifle should not accept the 308 diameter bullet, or at least I definately would not try it. If you can figure out a powder charge that would reduce the pressure to the operating range of 37k psi with a .299 diameter bullet you might be able to make it work.
Regrettably, this Model 89 sounds like a wall hanger. Sorry. Mikey.