You can call it whatever you want but it won't resemble a #8 if you make it to fit a 1581XL action. The only thing that will be the same is the muzzle diameter. I think an .820 muzzle is big enough but I don't like the way a barrel looks with that much taper.
I checked a while back an if my memory is working, the barrel Krieger makes for Surgeon is a modified #10.