I think I've done everything you lined out plus a little more.
I bed my action with the tin from a pop can and shimmed the sides of the block that the back of the magazine clips into. This action tightened up the magazine lockup plus gave a better bedding for the action. after I put a Shaw barrel on mine, I went back and using some Devcon, I skim bedded over the pop can tin. On the back of the barrel there are cutouts in the barrel that fit into two tabs in the action. These cutouts and tabs act to align the barrel in the action, but I thought they may also act as a form of a recoil lug, so I made sure I put the Devcon in this area so it had a tight fit. The tin with the skim of Devcon over it gave me a bedding that is continuous on the entire action.
Some find the rifle is a little more accurate with the thread protector off the barrel. The way the thread protector is made and goes on the barrel forms a little chamber at the end of the muzzle. I enlarged the hole in the thread protector and my rifle shoots the same now with or without the protector in place.
The Shaw barrel most defiantly improved the accuracy. I think the reason for this was the match chamber in the Shaw barrel verses the "Sporting" chamber in the factory barrel. When I chamber a round in the Shaw, the rifling engraves the first driving band on the bullet, so the barrel/rifling holds the round concentric to the bore. In the factory barrel, with it's generous chamber, the only thing that holds the round anywhere close to bore concentricity is the ejector holding the round to the bolt face, and/or a build up the carbon ring in the chamber, all of this is not conducive to repeatable accuracy. If the carbon ring isn't uniform, or you get a little carbon on the bolt face, the round isn't held straight in the bore. Further, in a sporting chamber, the only thing that allows pressure to build before the bullet begins to move into the barrel is the crimp on the bullet. With a match chamber that engraves the bullet, pressure has to build to a level that both overcomes the bullet crimp and the resistance of the rifling engravement on the bullet. My velocities with the Shaw barrel are both higher (about 20 fps faster) and have a lower standard deviation in velocity than with the factory barrel, and I attribute this to the extra resistance the rifling engravement has on retarding the release of the bullet from it's case.
I also use Butler Creek Magazines as I feel they do a better job of feeding the rounds straight into the chamber.
I also added a two stage Timiney trigger, but I don't know if that has helped with improving measurable accuracy. I mostly shoot for groups at 50 yards but with all the things I've done to my rifle, the groups at farther ranges have improved, but I as I haven't measured them, but they look smaller.
