Robert,
Unsurprisingly, your sketch confirms the standard 8x50R Mannlicher chambering.
Despite the .329" groove diamater Austrians used .323 bullets. Today handloaders are using long heavy flat-base bullets of this common diameter with good results. Some use .329" bullets as mentioned by Mike and some even go to the trouble to squize .338 bullets down to about .330".
A couple of additional notes. A friend noted from the photographs that your rifle uses the M90 carbine receiver, not the standard M95. The M90 carbine receiver has a higher rear bridge, similar in shape to the receiver ring, while the M95 has a lower and flatter rear bridge. Another observation is that your hunting rifle seemingly uses a longer barrel than the usual 20" carbine tube. Could you measure it?
Cheers,
Jani