Re: Moving up to mid long range
Welcome and sounds like you are heading in the right direction. Get a Leica rangefinder so that you can range accurately and quickly. Work up accurate, reliable loads. I would lean to 155gr Amax/MK, and 165gr SST for your work past 300yds. Varget is a great powder for the 308Win case.
Lots and lots of practise from field positions at the ranges you want to hunt. Shoot under any weather condition you will hunt in. Learn to dope the wind.
After that, the hunting part is pretty straight forward. Set up, see game, range, adjust for conditions, take shot, clean animal.
I am surprised that you can hunt that far in Italy. Was there and got the impression that there was a house or town every 100yds or so.