I glanced through this post and a few things hit me. To start what is a "loose chamber?" My question is why wouldn't a fired round fit back into the chamber it was fired in? I would be upset if the round would not chamber back into the chamber it was fired in. The manner that Savage chambers barrel, can lead to the chamber being crooked, and you can tell this when you jamb a bullet and it will only partially mark the bullet. The thing is I have seen many of Savage rifles with crooked chambers, and it don't seem to hurt them any as far as accuracy goes. I would say that some of the best shooting Savage barrels I have seen had crooked chambers.

Now moving onto the accuracy problem, to start why are you shooting 5 shot groups? 3 shots proves the load, 5 shoots proves the shooter. Onto of that your shooting a sporter barrel ,and I would imagine that with 30/06 rounds the barrel heats up fast. This gun is not a Benchrest gun, don't treat it as such. Even with our Benchrest guns when I am looking for a load for a barrel we only shoot 3 shot groups, until we find a good load. Most accuracy problems come down to optics. Just because a scope is new, or a certain brand doesn't mean that it is good. Try another scope and see if it makes any difference. Also check to makes sure the mounts are tight, many aftermarket basses have screw that are too long, and bottom out on the barrel threads before the tighten down the bass.

What is a "called flyer?" I have heard this term used, but it makes no sense to me. If you know ahead of time that a bullet is going to be out of the group why would you fire it ? In my world a flyer is a flyer, meaning it is out of the group because either some was wrong, or the shooter made a mistake. In competition no one will let you get a do over because you called that flyer.

Seating depth is the most critical thing when dealing with loading, don't just try one depth. Powder charge is less critical. Don't get hard headed when dealing with seating depth, try everything from a hard jamb to jumping the bullet 95 thousands. Some barrels like the bullets jumped. Also pay attention to how the bullet mates up with the seating die, this can cause uneven seating depths, and concentricity problems.

Last try different things when cleaning the rifle. I have found ever factory savage barrel I have ever shot, shot better when it was dirty. I have found that most savage barrels open up groups when they are clean and it takes a few shots for them to settle down. Don't "fire lap" your barrel, all you will accomplish is extra wear on the throat and lead angle of the barrel.