I'm not going to try to talk you out of doing this project, but WHY ARE YOU DOING IT?
If that barrel were full issue length, even the K version, the project would be worthwhile.
If that barrel has been significantly shortened as you say, all you're going to gain from this is changing that rifle's status from commercial ammunition available to reloading only.
You won't gain anything but more recoil and more muzzle blast. Velocities will be much the same, with maybe a very slight edge to the original chambering.
The 8x57, when it's hand-loaded to European specs will do anything a 30-06 will do with similar weight bullets.
You don't mention if it's a .318 J bore or a .323 JS bore.
Many hand loaders don't know there is a difference, so reloading manuals in North America list LIGHT loads in case some nimrod shoots .323 bullets through a .318 bore.
I would suggest, before you bugger this rifle up, load it to the European pressures and shoot it. You will be surprised by how good a round it is.
I load for two 8x57 sporters.
One is a put together, utilizing a sportered DWM 98 receiver, with a full length 23 1/2in barrel in excellent condition. It was a new in wrap replacement barrel.
This rifle will generate 2600fps with a 196 grain Oryx bullet, measured with a magnetospeed. It also delivers moa or less accuracy with that load.
The other rifle is a Husqvarna I bought from Eagleye a few years ago. It has a 22.5 in bbl and the velocities are 2550fps with the same load, and give the same accuracy.
IMHO, you aren't going to get much if anything more from the rechambering job you want to do.
On the other hand, if you're just looking for a learning curve project, fly at it. We all have to learn one way or another.