The silvery stuff will be graphite.
I've got factory bedded H barrel rifles (snipers), I've bedded a couple of H barrels myself using the some of the "old methods" described in the books by James Sweet (many dozens of hours). I have a fullbore rifle that was bedded in the thirties and is a proven competition rifle. I've even got a H barrel fully floated from an action mounted in an aluminium bedding block. Bottom line... Nothing beats a properly bedded barrel using the methods (refined) of factory bedding for a standard barrel. It can be very hit and miss, though. Another problem is, the woodwork can be unstable due to climate. A fully floated "H" barrel in good condition can be almost as accurate as the best bedded barrel, but more consistent. To fight this problem some old target shooters here used to hand make foreends and handguards from harder, older and dryer, therefore better suited more stable timbers. Use of cork or gasket paper packing was seen as the easy way out temporary fix or a method of getting a bit more life out of a buggered foreend. The cork was also infamous for eventually becoming compacted, hardening and cracking away.
The bedding starts at the butt socket. Just working under the barrel can just transfer the problem further back. The secret wasn't to try to lock everything up so it didn't move. It was to set it up so it moved exactly the same each time it was fired.