How precisely cut is the magazine? That may be your limiting issue, if the magazine cannot hold the larger diameter cartridge.
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Sounds like a Browning BLR takedown in .308 is what you are looking for!
KC - I have a M1899 Savage, formerly .22 HP, now rebarreled with factory Savage .30-30 barrel. Forget about the pointed bullets idea. Magazine limits OAL and requires much deeper seating of pointed bullets, thus reduced cartridge capacity, plus puts them way back off the rifling. In my experience COL for reliable feeding is is 2.500" - 2.525". The Hornady bullets for the LeverEvolution ammo might be OK. Otherwise Sierra 170 or 150 are most accurate, being closest to the rifling, which this rifle requires. If you want extra velocity, buy some LeverEvolution powder.