So I got this M-44 several years ago from a LGS.  It's a 1944 all matching Izzy in excellent condition.  The dealer did inform me that the previous owner shot only surplus ammo and didn't clean the rifle after each session and that it was no longer accurate. One MOA of steering wheel with surplus.  For $60 frn's, what was the harm right?  Now that these rifles are trading in the high 3's and low 4's for the condition mine is in, minus the barrel of course, I'm wondering if it can be repaired.  It's already counter bored and am wondering if it could be done again just a bit.  I scrubbed the barrel to the point of getting a bit of shine back and the lands and grooves aren't sharp but still very visible but still 1 MOA of steering wheel with circle 10 surplus.  I can get down to 1 MOA of pie plate buy using  203 gr. Barnaul loads.

Anyone know if there is a way to correct the issue without a new barreled action or a way to change the barrel and still keep the bayonet?

Are you fixing the bayonet when you shoot it?  Serious question.

No.  But I don't have to on my other M-44's to obtain accuracy of near 1MOA, from a rest, with 203 grain Barnaul.

Sell and replace with new toy.

This.

Also from what the OP is describing the barrel should still be pretty serviceable.  I would bench it, see where it's shooting and adjust the sights. Buy a Mosin sight tool if you have to, their cheap.

I would add to the suggestions here to try some different ammo, too.

Some rifles "like" different ammo.

That rifle might benefit from cast boolits. Might just need a fatter bullet.

.314 is a good place to start.

Slugging the barrel is the best place to start. Be sure the slug is consistent, as some war year manufactures have been seen to have widely varying dimensions in the middle of the barrel.

Try different ammo. Clean the gun even more. You may want to reload some for it

Shoot it til its a bit hot then clean it. Then shoot and see how it groups.

Make sure the receiver screws are tight. The front one VERY tight, the back one snug.

Some of these rifles benefit from having the receiver shimmed, I even glass bedded a 91/30 years ago that got .85-1.05" groups with reloads and iron sights.

You could also watch Youtube videos on how to "cork" the area under the barrel bands. But this tends to benefit the full length rifles more it seems.

Shoot it with the bayonet out.