Friend, I think you have the original stock right there. It's just that a woodcarver has got there before you.
The only Mannlicher-Schoenauer rifles adopted by the military were the Greek contract of 1903 and the later Greek rifles, all built by Steyr. They all were in 6.5x54MS.
The 8x56MS, the 9x56MS and several others all were commercial cartidges which never saw military service.
You have an absolutely beautiful old commercial rifle. Treasure it.
Somebody likely can recommend a stockmaker competent to make a stock for this one. It will cost a chunk of money for the work, so you may as well blow the bankroll and spring for a REALLY nice chunk of Turkish or Circassian walnut, do the job right.
Hope this helps.
.