So I have a Mosin Nagant M44, which has a permanently attached bayonet that folds in. If I shoot with the bayonet folded, it impacts a good 6 - 7 inches to the left at 50 yards!! If I fold it out, it seems to be windage dead on. How could the bayonet make that much difference?
Mrb is correct.
The Russians were BIG on cold steel. The older (pre M44) versions of the Mosin were intended to have the bayonet basically left permanently fixed, they didn't issue bayonet sheaths from what I remember. It was to instill the 'aggressive spirit'. More than one firearms expert has called the Mosin a .30 caliber bayonet mount. They wanted you to get in close. So yes, Mosins won't shoot to POA if the bayonet is not mounted, or in the case of the M44, folded out. Barrel harmonics are no joke.
Useless to fool around with the outside crown as it no longer has any effect on the accuracy. The real crown is the inside edge of the counter bore. If that's been screwed up by a cleaning rod you'll need to use a drill press, set the barreled receiver up vertically and run a drill bit in to get a fresh, sharp edge all the way around the bore where the counter bore cut hits the original bore.
I use a high quality steel 3/8 in. bit and motor oil as a cutting fluid. Make short cuts in but don't let it ride without cutting, keep the bit cool, stop when you've got that sharp interior crown with rifling visible all the way around it.
Also when you pull the stock off, check for warping and uneven contact with the barrel as that can drastically affect accuracy.
Some older surplus ammo is lacking in the accuracy department. The best I found was the silver tipped light ball from the '70s or newer.