I too would choose a peep sight over both your scope mount choices. Peep sights are accurate and user friendly to old eyes. I put a Lyman 36 sight on my 1903. A bolt peep would be good too. They seem harder to find than the Lyman 36.

Who says side mounts won't hold zero? My 1952 M-S came with a Paul Jaeger side mount that returns to zero every time. I don't think gun makers would be wasting their time for nearly 100 years making and fitting detachable side mounts that are useless.

It's your gun. Do what you want. Maybe you could have bought one of the plentiful carbines that are already scoped.