A little background on the rifle Bigwagon that you may not yet have come across: this is I believe the 1064th rifle built by Steven-Savage on the initial Britishicon contract and these pre-Lend Lease rifles were paid for in cash by the British government which is why they do not have the "U.S. Property" marking seen on later Savage No.4s. It's a significant rifle just for being that early, even without the (T) conversion. We've seen a few such early Savage rifles converted to (T) spec here, including 0C0001 and 0C0006 if I remember correctly. The MkI* modification was soon introduced at Savage as well as Long Branch; an ill-advised step, but that's another story.

You might try it at the range with the forend removed entirely. At that range with decent ammo they should all be in the X ring, if not the next one, if the barrel is in very good condition? The missing handguard is probably evidence of someone's abortive attempt to resolve the likely problem with the forend bedding which is causing that inaccuracy.

It's a bit odd that you have a No.3 bolthead fitted, but it may have been fitted by some civilian owner. We are told that a rifle that would only headspace with a No.3 bolthead would have been scrapped during overhaul or Factory Thorough Repair and judging by the finish your rifle has not had enough use post-FTR to need a bolt head replacement. If a civilian has replaced the bolt head it may well not have been done properly and that might also be a cause of the inaccuracy I believe.

You could check the squareness of the bolthead face by getting a good guality .303 "no-go" headspace gauge, coat the face with layout blue and close the bolt against it. The squareness of the contact will be visible in the marks left in the blue.

I assume the bolt number matches the rifle and appears original?