7.5x55 operates at well under 50k pressure, .308 operates at about 52k.
TEXT BOOK OF SMALL ARMS - 1909 gives operating pressure for the Swiss Model 1900 rifles and ammunition as 17.1 (British long) tons per square inch: 38,304 pounds per square inch.
LESS than a .303, which had an operating pressure of 18.5 tons.
Operating pressure of the .308 is 23.2 tons.
You are operating your rifle well above the pressure levels it was designed for when you shoot factory .308. Handload and drop your pressures a bit through use of a progressive powder.
Problem will disappear..... or should, anyway.
There are different variants of Swiss 7.5 rifle rounds
GP90, 1890, 7.5x53.5, 36000psi
GP90/03, 1903, 7.5x53.5, 36000psi
GP90/23, 1923 7.5x53.5, 38000psi
GP11, 1911, 7.5x55, 45550psi, with the first(?) VLD bullet.