Hmmmm...
Sanson1--Random thoughts: From yr description of the problem, it would seem that a break-in procedure would indeed be in order.
You know the drill: Fire one, clean bore, repeat 5x,
Fire 3, clean bore, repeat 5x,
Fire 5, clean bore, repeat 5x, that should about do it.
David Tubb makes a "fire-lapping" system, bullets embedded with finer and finer abrasives, which is supposed to be great to smooth out a rough bore. No first-hand knowledge. Sold thru Midway, I believe, among other sources.
Anyhow, as to break-in, that'd come under the "Can't hurt, might help" category. Fire-lapping might be the next step.
This is a brand-new rifle, right--Not just new to you? No obvious crown damage?
Have you contacted Savage about this--What do they say--They SHOULD know how that bbl wants to be treated. Mebbe contact Savage as a FIRST step.
Now, having said all that, the .243Win has a reputation as a "fussy" cartridge for handloading. Mebbe what you're experiencing is a manifestation of that--Have you tried more than one load/bullet weight in it? (Personally, the 2 .243's for which I have loaded were happy with just about anything I fed them, but the reputation remains. And N=2 is not a "statistically valid" sample.)
Guess I'd start by asking Savage about it. Generally Savage rifles have a reputation for no-nonsense accuracy. What model is yours?
Anyhow, good luck and keep us posted.