Worth a try.
Ken Waters loaded 7x57 with a 150 gr cast bullet and 21 grains of IMR 4198 for 1722 fps. That is a pretty stout cast bullet load - for the bullet, not the rifle - and I would try something like 18 grains. You might have to raise the muzzle before each shot for any sort of uniformity. DON'T use a "filler." I don't know why the Lyman Cast Bullet Handbook shows only pistol powder loads; the regular Lyman 47th has cast bullet loads with rifle powders... but not 4198 in 7mm.
Sandy is right, you can have fun with a very light load of pistol powder and a velocity around 1000 fps. I have shot the Laser Cast 165 gr .30 cal in .30-06 with 7 and 12 grains of 700X. It is accurate in my sporter but not my target model M70. The 7 grain load has almost no report or recoil, but it will shoot under 2" at 100 yards.
Accuracy with commercial cast rifle bullets is spotty. If the ones available to you do not do well, try light loads with jacketed bullets. It was made for FMJs and I doubt you will be shooting that RB enough to wear it out. The Lee book has a formula for computing reduced loads that works pretty well, and Hodgdon recommends H4895 for reduced loads in bottleneck calibers. A 150 at 2000 would be ok.
The 7mm RB is widely reported to have excess headspace by modern standards. Did they change the specs? Probably not, I've never heard such a warning about a Mausers, early or late manufacture. Are they built sloppy? They are Remingtons made to real mil-spec, seems doubtful. Did the guns wear that much? It seems unlikely that ALL 7mm RBs would have been used that much. Did Remington fudge the dimensions for better operation of a rimless smokeless round in a old design single shot? Ah-HA! No reloaders in the Mexican army, after all, and you can get away with a lot of headspace if you don't plan on reusing the brass.
You can make the brass last by neck or partial resizing after it has been fired in your rifle.
