If you have access to a Sierra loading manual,they have both .308 Norma and 30-338 pages,along with cartridge drawings.
Norma created the .308 Norma product with(my understanding) no rifles commercially chambered for it initially.
They had a program where they rented reamers to gunsmiths who were doing their bread and butter job at the time,converting mil-surps.Normacreated an ammo market.
It is slightly shorter than the .300 Win mag.IMO,it is a little better as far as having room in the magazine to seat the bullets out a little further.
After forming the cases,check length.They could be a touch short,as I recall.I suggest just a minimal cut with a case trimmer to square and uniform them.
While it may be possible to retrofit it back to 30-06,and Criterion makes a good replacement 1903A3 bbl,
A bolt and extractor will be necessary,but what may bite you,sometimes a little work was done on the feed rails for the fatter belted cartridge.
If so,you may find the 30-06 rounds spew out the top of the action.