I have family members that have killed uncountable number of deer & other game with the .300 Savage in the 99. It is an excellent cartridge/gun combination & there is very little if anything to gain converting it to a .308. If you'll try it on deer & hogs I'm sure you'll realize that rather quickly. Use the money you save not converting to start reloading. Then your .300 will be suitable for everything up to caribou with the right load.
Looking in several loading books for 150gr bullets (best bet for deer & hogs):
.308 Win max velocity is 2700 to 2900 fps
.300 Savage max velocity is 2500 to 2700 fps