Yes this site is great for these rifles. Lots to read.
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Can you post fairly closeup photos of the left side of the receiver Togor, without the scope bracket fitted and with it fitted?
The buttstock bolt is tight, but not protruding through the front face of the butt socket? (Looking along the forend strap with a bright light will help.)
The trigger guard screws are tight?
The barrel can be pushed upwards slightly and to the left and right slightly at the muzzle end?
The bracket, scope and rifle are numbered to each other?
Not to insult your knowledge or intelligence at all by the way.
Suspect it is a standard No4, rather than a 4T.
Belay that; I had the impression you had a Maltby T you were having trouble with.
If you have HS gauges in .303 you could put layout blue on the bolt face and close the bolt slowly against the no-go gauge to see if the bolt face is square to the chamber.
The other obvious question is whether the bolt is original or a replacement and if the latter was it done properly in a FTR or just swapped in by some civilian owner.
Bolt SN matches. The fired brass looks concentric. More generous like a MG chamber than a US cal. 30 rifle chamber but I think with annealing and judicious resizing it could be reused.
I can try something like your test with an unfired case.
Use a Lee Neck collet die, only use a full length body die when chambering becomes very firm and then sparingly.
A properly sized cast bullet does miracles with oversized worn barrels.
Use the Hornady 150 gn .312 FBHP they are pretty good shot them for ages I found they fly pretty good up to 400m I used them in my 2 No.4's with 2 groove brls and my 1945 OA No 1 MkIII I seated them with @3/4's of the cannula showing and then medium crimp.
See pic of one of my rounds just check the fit in the mag allowing enough for functioning & recoil.