I would consider getting mine resleeved back to non-shot out condition if the price was right.
The barrels on broomhandle pistols, are very thin. Installing a sleeve is a recipe for disaster, no matter how it's done.
The only successful jobs I've seen, were done by cutting off the existing barrel, chucking up the upper in a lathe, machining out the existing chamber, leaving enough room to cut some internal threads that will match a pre chambered make up barrel and put them together.
Even this method has to be done with extreme care. There isn't a lot of metal there to play with and you want the chamber area to be as strong as possible.
Installing a newly made up "WOLF" spring kit is also a good idea. I recently purchased a broomhandle from a fellow CGNer. All of the springs in the pistol were either broken or collapsed. He says he didn't realize the springs were bad. OK, he has a good rep and likely, only picked up the pistol to flog it. It had obviously been used to shoot the hot Czhek 7.62x25 until it no longer functioned properly.
I magnafluxed the receiver and upper and found it sound, with no visible cracks anywhere. The bore was VG so it was worth the effort to get it functioning properly. I load 100 grain x 30 M1 Carbine bullets of .308 diameter. It shoots them quite well, considering that they are a couple of thou to small for the bore diameter.
This looks like a hi jack, sorry but it is intended to give an example of what can happen with these old girls.
They are not something to consider as a project gun, if you have to pay someone to get them shootable.
They also need to be fixed properly and not just partially.
They are very well designed but they were never intended to have their uppers rebarreled or repaired. Likely, at one time, the uppers were available as a spare part.
This has been going on for at least 50 years that I know of and likely even longer. There was a time when you couldn't get anyone to buy one with a shot out barrel, because of the difficulty in repairing it as well as the lack of parts for the rest of the pistol.
If that were my pistol, before I would even consider rebarreling it, I would look for another upper in decent condition. You're losing all collector value anyway. Also, I would have the frame and some other critical parts checked very carefully by someone that know what they're doing.
There is way more to this project than just getting a new barrel installed.