Like so many others here have said, your brass is fine, a little less lube to get rid of the dents and shave a little off your case holder or die. Do just a bit at a time till they chamber nicely. I had to do that with my 6.5 PRC. I took the die to the side of the wheel on a chop saw. Not very...
I have a 22-250 push feed with the same problem. Has been that way forever and I have just learned to deal with it as it is my ol coyote killer. I will give Jack First a try. Mine just drops the shell when it clears the chamber about 50 percent of the time. Just basically falls on the magazine.
I agree on it not being one of Savages better works. I won one in a raffle and had it for a while. It was the light barrel version. Loved the cartridge but not the rifle. Pretty cheesy made. Kind of like some of the Savages of yesteryear. And it didn't shoot that well. Was always throwing...
Coyotes 8 and 9 since I've been calving. First with a 264 mag at 300 yrds. Apparently it didn't like that stuff hanging out of it's side. Lol!! Second one was a frontal shot with a 243 and Barnes 85 gr TTSX at around 100 yrds.
I think the biggest factor in this, after knowing your rifle and how it shoots, is the range finding factor. Anybody that has had any experience with range finders knows that they can be very finicky ranging on certain objects.