Do what you want, but cutting the barrel like you suggest is one of the reasons classic Ithacas keep going up in value- people destroying nice shotguns with hack saws.
Given a reasonable value of around $500 now consider:
1. Polychokes may look funny, but they are period correct and they WORK. They really work. First, pattern that gun and see if in fact it's not a nice hunting American pump gun with hand checkered walnut and smooth as silk bottom ejecting action.
2. Mossberg's Maverick 88 has great reviews for what it is- sturdy, reliable, out of the box ready to go and you can get a new one for $200. Yes, new.
If you want to rebarrel, first you need an old "new" barrel of the same vintage- not the newer ones. Then it's hand fit so that when installed, the shell headspaces properly. I expect that with some luck, some drop right in. Others will need to be shortened such that the 1/4 turn of thread headspaces correctly. If the barrel is too short, it might become some creative lathe work. Too long, easy peasy. I have never done it. The cost of rebarreling I expect is about $500 or two and a half Maverick 88s.
You're going to ruin a nice collectable hunting shotgun, but it's your gun.