It is not as hard as it seems. I wanted to do this a few years ago but couldn't find any one to do it. They were either way too expensive (over $1000) or had never done it and didn't want to try. I called a local smith here who does a lot of rifle work as a hobby. He is a retired Sociology professor from one of the colleges here in North Louisiana. He gave me the same song but with a different verse. He first said he had never done that before but he liked my idea. After examining my rifle and looking at an exploded diagram, he felt it would be no problem. He ordered me a stainless Douglas barrel, turned it on a lathe to proper dimensions, cut the dovetail in the bottom to mount the screw stud to attach it to the stock, and even stamped the barrel with gun make, model and caliber. Cost was $300. Turnaround time was 2 weeks from the first day I took him my rifle. Now I have a Post '64 Model 88 with a blackened stainless Douglas barrel 23" long (factory is 22") with no sights. I have a Nikon Prostaff 3X9 on it. It went from being a .243Winchester to a 7mm-08. It shoots a 1.5" group at 100 yards with Hornady LIght Magnum ammo. It is my absolute favorite Whitetail rifle.
The Winchester 88 is no harder to re-barrel than any bolt action rifle. You just have to find a gunsmith who is willing to look at the rifle long enough to figure that out. The harder thing is to find someone who can do a trigger job on them. They can be smoothed up a little but that is about it.