I've got an old Savage 30-06 that I picked up at a pawn shop. At some point, languishing in my safe for over a decade it decided it didn't want to feed right anymore. The rounds on the left side of the mag pop out prematurely and try to fly out of the chamber. Might have been nothing more than a weak spring but I tried closing the feed lips. It' so boogered now, and still not feeding reliably, I just want to replace the assembly. Looks like the box is staked into place. Is this something I can replace myself or should I send the whole rifle back to Savage?

You can convert it to a detachable mag and buy a new stock and bottom metal. Savage will tell you they don't have parts for a long action, blind mag, stagger feed.... to convert is expensive. New bottom metal can run $200+ stock.  Sign up on savage shooters forum and check classifieds.

IIRC, it's not staked, but is tabbed into slots in the receiver. Savage blind box mags are cheap, and if you take a more in depth look at the gun I think you'll figure out how to replace the magazine. Do yourself a favor and replace the mag spring and follower at the same time.

Does Savage have the parts or do I have to go somewhere else?

I bought my last round of mag parts from Midway. They've had everything I've ever needed for the 110, including the newer style bolt heads.