When looking through a bore scope all factory rifling is ugly but that does not mean they will not shoot. That crown needs some work---not good.
The flyers are most likely because of bedding issues and as latent stress makes itself apparent as the steel heats up. This is just something to accept with a factory barrel unless you let it cool between shots with respect to the stress issue.
The Truth Is Not Always Good For Business!!
I don't think that group size is from the crown, but will agree that it needs to be redone. Groups look like something is moving during recoil. Whatkind of bases and rings are you using, and did you bed the base (s)? I'd hunt up a good 1/4" drive inch pound torque wrench that falls into the 25 to 60 inch pound bracket (around zero to seventy-five inch pounds). Torque the bedding screws to about 35 in.lb., and try that to see if it helps. If it dosn't, then torque them again to 40 in.lb. Then once again try it at 45in.lb.
Back to the barrel: I hope you are not useing metal brushes! Have a good one piece cleaning rod with a guide. I like the stainless steel Pro Shot rods pushed thru a tight fitting guide from the chamber. I don't personally like coated rods, but others think differently I know. More crowns are messed up from cleaning than anything else. Never try to pull a jag or brush back thru the crown.
Take a good serious look at the barrel with a good tight fitting jag & patch. Coat it with light oil, and push it thru the barrel making note of the tight and loose spots. If the barrel is tight all the way till the last three or four inches you have a problem. But if the barrel is nice and smooth till the last four inches, and get's tight you have a good barrel to work with. If it's pretty much the same all the way, I'd be looking at lapping the barrel. Maybe a few bullets coated with 5a lapping compound might help here.
This rifle comes with HS Precision stock, I do agree I need to get it skin bedded, right now it has Weaver 20 MOA rail I didn't do any bedding on it, I took scope with rings from my 308, it has Weaver rough looking 4 screw medium rings, never had problem with that thing moving. The action screw, the front one I set to 35 inch/lb rear is set to 30. About Weaver rail, before that I had 2 piece standard Weaver rails, they produced same result. What I noticed there are aluminum lines from bedding block printed on the sides of the action, after I get it skin bedded they should go away.
A number of years ago I sent a unfired 338 barrel to Savage that looked like your barrel. I knew it was going to foul bad. They told me there was nothing wrong with the barrel and to quit using a bore scope. I refused to resell the barrel and I refused to shoot the barrel until after I sent it to Benchmark and asked the guys to clean it up.
They pinned the barrel and the pin would not drop through the barrel. $35. for lapping and I have avery fine shooting barrel.
That crown is bad.
The barrel in this picture has hand lapping performed not to abrasive just some KG-2 (1200 grit), so it is not as bad, I haven't try it yet so it might not have as much fouling as I experienced previously.
I doubt anything moving because of the recoil, since after I clean it repeats same pattern. However I took my other rifle Rem 700 in B&C medalist stock and I played with torque on action screws, having front to 35 inch/pound and back to 30 I had fliers all over, but when I set front to 50 and back to 40 the accuracy return to 0.36" 5 shots.
I think I'll make few loads and test drive Savage with torque wrench.
About cleaning, I don't have any metal brushes I only use nylon from Boretech, jags are also from Boretech. For cleaning rod I use Tipton carbon fiber cleaning rod and bore guide, never insert anything without one, any time brush comes out from muzzle end I remove brush, the jags are different after patch is removed, I do not remove jag, just pull rod with it.