I have a Spitzer SA that also has a sloppy blade to crossguard fit. However yours appears to possibly have either a grip or crossguards replacement.
My reasoning: Looking at your last picture where the grip protrudes past the crossguard and assuming the crossguard is correctly installed. I would expect this exposed area to be darker than it now appears after 65+ years. Additionally; If you remove the crossguard I'd expect there would be a difference in coloration between this exposed area and the protected area under the guard.
However it is possible that if you flip this upper crossguad around the fit would improve.
Jim