The .300 is a fine round, but I can see no practical post-.308win reason to get a rifle chambered as such for hunting unless you already own an M99, M81 or other and want to use the same load in both. There is perhaps a tiny niche in IHMSA silhouette, where the reduced case capacity can work in the shooters favor, or in the case of rebarrelling an older weaker action such as Mauser 95 or MS1903 to prevent full power .308 from being used. I suppose a .300 Sav in a longer magazine with a fast twist, really heavy bullets and a suppressor could be interesting too.
Handloaded, the .308 can absolutely be loaded to ballistically equal the .300 Sav with no noticeable loss in accuracy or consistency (I do exactly this for my wife's .308 Savage M11) with near infinitely more loading options in terms of bullet profile, weight and length, load data and brass availability. The Savage cartridge is somewhat handicapped with "long" bullet profiles due to the short magazines, short neck and limited case capacity. It's at it's best with old fashioned (to some, not me) 150 to 165 flat based spitzers or the 180 round nose.
A build will be significantly more expensive than a new or used rifle in .308 with little or no gain in performance, but it's your money, so if you really want a .300Sav, have at it, the reamers are out there and anything that is/was ever offered in .308 will make an acceptable donor with no modification of bolt face or magazine required. I'm sure you can find a gunsmith that will do the work. For my money, I'd shop for a good Rem 722, a vintage Mauser or MS, or one of the Rem 700 classics chambered in this round, in fact I saw a matched pair of Rem 722s this weekend, one in .300, one in .250.