Here's my advice.
Go home, scrub the barrel out with solvent and copper cleaner.
Go to wherever and buy the Fed GMM in 168g. Shoot 2-3 fouling shots and then shoot for groups.
I see no reason why this setup should be shooting over the 3" mark. Should be good for 1" or 1.5"
The human mind can play tricks. My guess is that you were so worried about the thing functioning, and all these new variables that the 1" group was never going to happen.
I pencil barrel will "open up" group size when hot, but then quickly shrink down to previous accuracy standards when cool. The POI shift with pencils comes from the old school handguards attached to the barrel, when they heat up they apply pressure on the barrel in different ways. Free float barrels dont do this.