Thanks to all for your replies.
I made a crude set of "V Blocks" from a set of automotive axle jacks that I had lying around the garage, and removed the barrelled action from the stock. I just wanted to be able to rotate the barrel on something that might show a bit of runout. No dial indicator, or any other measuring device as of yet, but the barrel does appear to have a slight runout, and certainly enough to affect accuracy.
I have found a couple of used barrels online, apparently it is impossible to get a new one...
There are 2 solid pins driven into the action that hold the barrel in place, are these a heated/interference fit? Is the barrel to action coupling a heat/interference fit as well?
@ Blastattack - thank you for your offer, but I think that I'd like to get a 581 barrel. The gun already has a globe front and redfield match rear sight.
I learned to shoot on this firearm, starting at 12 yrs old going to the gun club with my father. So, I'm trying to get her back into shape as a nice useable piece, and for sentimental reasons.
Thanks again for any helpful info