You may be able to take a round stone and just take a very small amout off the top edge of the chamber, just barely break the sharp edge.
Remember, the chamber has to support the cartridge.

A better answer would be to adjust the feed lips of the mag so that the bullet goes in at a slightly lower angle.

I only have the problem and not every time on the very last round being fed from my 10 round mags.
If I go easy, it does not shave lead.

As far as accuracy goes, the Savages are great right out of the box.

Mine shot in the low .4" range with Wolf ammo, 5 shots @ 50.

I took it to Savagegunsmithing for an accuracy job and when it was returned, it shot a best of .117", 5 shots @ 50 Yds.
It will shoot in the .1" range on a good day with little wind. If it's a little breezy, it shoots in the .2" range, or sometime .3" if it's more than just breezy. The trigger is now a totally safe 8 OZ and breaks clean as glass. It still looks like a stock sear and the other parts still look stock, though the springs have been tweeked some, so there are none of the shims or some other sear mods I've seen posted that make me very nervious just to look at.

It really makes the Annie and CZ shooters made to see my targets, to think that a lowley Savage can shoot with or outshoot their expensive rifles. Mine is a .22LR BRJ.

By the way, it's nice to be back on the site, I was the Gunsmithing Moderator here on this site about 5 years ago. I intend to send my money in and be a paying member asap. I hurt my back and sold my gunsmithing business at that time.
I kind of slowed way down on my shooting for some time, but have got back into it big time. I'm not going to get another license and open another shop, it's just too expensive, but it's just darn nice to get back on this site. Always had a bunch of great people here.

Best Regareds, John K