Throats on military 7X57 rifles are quite long, with a very gentle taper. First thing, make a cerrosafe cast or an impact impression of the throat. Size the bullet to that, not the groove diameter. What is causing your headaches is gas cutting while the unsupported bullet flies through the throat area without some way to get a gas seal. If you have some way to recover bullets without damaging them you will see cut marks on the sides where they were torched away. You may find you have to invest in a custom mould designed to properly fit your own rifle. Veral in the other room below is a great source for those.
BUT...
Likely you will be able to shoot that bullet if you use some kind of granular filler. I like cream 'o' wheat, but I live where the humidity is very low. Other people warn against it because it turns into a rock when moisture is present. A good alternative is plastic shotshell buffer, which doesn't absorb moisture. If you have some slow powder like 4350 or slower, try about 25 grains of it and enough filler to make a lightly compressed load. Seat the bullet out as far as you can. Likely it will barely be in the case and still not touch the rifling. If you can get it to engrave all the better. Try a couple and I think you will be pleasantly surprised. You won't even need gaschecks because the filler completely seals the gas.
Be careful with this. Only use slow rifle powder, never anything faster than 3031 with filler. It will raise pressures considerably, so use only half the powder you would use for a full load. Used intelligently, it works wonders to make cast bullets perform. Paper patching will also solve your problem, as well as allow you to load cast bullet to full military ammo performance. But that is a subject for another time.