[Jack]

Sounds like you have a nice old rifle to play with!
Your described method of necking up 7x57 cases to 30 caliber and then necking them down to 7mm to create a false shoulder will work - use standard 7x57 dies to neck back down - back the 7x57 sizer out of your press until it just barely begins to size the neck down, then try the case in the rifle. You will have to adjust the die down and try the case in the rifle several times before you get the cases to just barely fit in the chamber.
Then load a moderate load in the cases and fire form. After that, you have cases that fit your chamber.
One tip: start with new brass. New brass is more elastic than brass that's been fired before - you will get much better fire forming with new brass.
The old rolling block action isn't as strong as modern actions, so keep the loads moderate. The original military 7x57 load was a 170 round nose at about 2200 fps. That load is likely what the sights were regulated for.