First I've heard.

Try shoving a .375 bullet into a case mouth that was fired in your rifle.

Trouble with hand loading for the 9.3x57, is there is no CIP law for it. Most stats, as in http://kwk.us/pressures.html use Norma stats which were ridiculously low in ballistics and pressures compared to the other ctgs. chambered in the same rifles, whether model 96's, Model 94's or Model 98's.
" 9.3x57 (CIP) 44 (PSI) (CIP) 38(CUP)

3 other rounds chambered in the same rifles, have CIP PSI's of 57,000.

As to your problem with the large chamber neck diameter, I would use .30/06 cases or even .35 Whelen brass, shove the necks back, trim to length and load one round. The brass neck will be too thick for a normal 9.3, but better suited to your larger neck than proper 9.3mm brass.

Make sure you anneal the case necks and shoulder AFTER making them up.