Beautiful rifle, great cartridge!!!
Uses a very similar belted magnum cartridge case much like the .264 Win. Mag, 7mm Remington Mag., .308 Norma Mag., .338 Win. Mag., .358 Norma Mag. and .458 Win. Mag., the 7x61 S&H cartridge appears to have a double-radius shoulder much like the 7mm Weatherby cartridge.
Generally, rifles chambered for the 7mm S&H cartridge are free-bored like the rifles chambered for the Weatherby cartridges. I believe your Shultz and Larsen is free-bored, but to be sure... check it out.
Full 7mm Sharpe & Hart maximum loads REQUIRE a free-bored rifle to be safe. Reduce all listed 7x61 S&H loads by at least 5% if the rifle lacks a free-bored barrel.
My old reloading manual (circa 1970) shows a maximum load of IMR4350 (64.0 grains, a compressed load) behind a 139 grain Hornady Spire Point bullet sparked by Remington 9½ primers in Norma cartridge cases yielded a muzzle velocity of 3257 fps out of their test rifle, a Shultz & Larsen 65DL w/ a 24" barrel which had a 1:10 twist.
My reloading manual shows loads for the 120, 139, 150, 165 & 175 grain jacketed bullets. If you can't find any other source of loads, PM me indicating what weight bullets you intend to use and I'll send you this old reloading information I have, but remember... these loads use the components circa 1970
... and current components may or may not yield the same pressures/velocities.
Strength & Honor...