My first recommendation would be to experiement with wrist pressure and feeding speed with the mag you have - Savage actions are not well regarded in field-style matches due to the exact issue you are experiencing, they are sensitive to technique under ideal conditions and behave poorly when conditions are less than perfect.
To start, try applying light downward pressure (i.e., gently take out all the slop in the bolt in the downward direction) and go medium-slow to give the round a chance at popping out of the feed lips and lining up with the bolt face before running out of play and running aground. With some experimenting, you can find what combination of taking out the slop and feed speed works least-worst for you.
If you're curious to try other options, I have had unreasonably good luck with polymer MDT 10 round mags as well as the Amend2 12rd magazines. I've been using those Amend2 12 rounders in local matches for a year or so, and honestly, aside from the length of them, they work great, in both factory rifles and custom actions. Given that these some of the most affordable AICS mags out there and are appropriately COAL limited for your factory action, if you must spend money, at least start small.
If none of those work, my next recommendation would be looking into adjusting how high the rounds present to the bolt. Things like metal magazines (thinner feed lips) and replacing/adjusting your magazine catch to raise or lower (probably not lower but you get the point) the rounds so they have a better path to the chamber. This is also the step where you could start modifying magazine feedlips on metal magzines, but that's a rabbit hole I'm not sure I would go down for a Savage action feeding a 308ish cartridge, that sort of thing is usually for BR/Dasher/etc cartridges.
I would actively recommend against anything meant for long COAL, such as "Binderless" magazines from MDT or Accurate Mag. Those are for actions and feedramps designed specifically for longer COAL, your Savage is not on that list and you'll have even more problems.