I've posted about this but do not remember posting a thread.
I bought a vintage Deerslayer barrel off of eBay to put in my older Ithaca 37. The barrel went in but there was too much headspace. So after looking for some answers and reading about a surplus Model 37 that blew up because of the wrong barrel in it, I contacted Diamond Gunsmithing via their web site.

Les responded and seemed sure that putting that vintage barrel in my 1959 37 was doable. And after reading posts here I've been patiently waiting to here from Les. Well the phone ran yesterday, a call from Ithaca NY, and we were in the middle of doing a transfer so my mind was on that, but then "shotgun" & "Ithaca NY" connected in my brain, and it was Les.

He informed me it was a go, so I'm pleased with that.

My Model 37 is interesting in that Dad had bought it new in 1970, and I never understood why my Ithaca didn't have interchangeable barrels, until I found out it was made in 1959 IIRC. Being an overzealous kid I managed to overtighten the magazine nut and eventually the barrel lug popped off. I had it welded and that didn't work out so well. Quite a few years later I sent it off to King Ferry for new wood and barrel. They did a nice job but I wasn't overly pleased with the results.