I really don't know what it could be. It may be something that just wasn't made exactly right on the gun or it may be something similar. Has it always grouped like this? You said it only has 60 rounds or so through it? Instead of just running breakfree patches down the barrel I'd try a copper solvent when cleaning it. I use Wipe Out patchless bore cleaner personally but there are lots of others out there too.
As for the ammo I'm not really sure. I see you say white box Winchester do you mean the gray box of Winchester Super X ones that usually say either soft points or hollow points? This is usually pretty decent ammo if that's what you mean. If it's some bulk stuff in a white box I'm not sure about it. However, I would try others too. I know with my rifle which is a Browning BAR hated the ballistic tips from Winchester and did exactly what you are describing. It liked the Super X soft points better but not that well. I then tried Remington core lokts and it also didn't group so well. I then tried the Federal Fusions and while the shots aren't always touching I can sometimes get them touching and it seems like I can pretty constantly keep it under a 2" group and usually around a 1.5" group. This is a lot better than shooting all over a 8" target as the ballistic tips were doing. I also found that the Federal Power Shok Soft Points for $14 a box at Walmart also shot well in it. I was surprised that changing to a different brand of ammo could make a difference but it seems to have.
Another big thing is are you waiting for the barrel to cool down between shots? If it's getting hot the groups are going to open up. Make sure you let the barrel cool after a shot or two.
I will say when I shot the 5 shot group at 1.5" I didn't let the barrel cool very much and it still shot that. I did have a 6th shot that was a flier but I think I pulled on that. This is something you have to keep in mind too. I've seen personally how groups can really open up once the barrel gets hot.
Overall, I'm not really sure that there isn't something wrong with your gun so you may want to see about having a quality gunsmith look at it or seeing if Savage will do warranty work on it. It's for sure not normal for that gun to shoot groups like that. However, these tips are something you can try yourself if you want to see if you can get it figured out on your own.