"The sleeving of new barrels in an old shotgun,be they rifle or shot, is best done by cutting threads in the front 1" of the hole "

With the greatest of respect, there is insufficient wall thickness to do that to a best shotgun if one is replacing with shot barrels. Given that the barrel shank diamiter needs to be less than the minor diamiter of the thread and then the major diamiter needs to be accomodated by the existing barrel wall thickness. Nor is it needed as it will not conceal the joint. Traditionally these sleeves are simply soft soldered into the reamed out "monoblock" created by cutting off the old barrels. The resultant surface area for the soft solder give much highter sheer strength than a fine circa .729 minor diamiter 1" long thread can do. Further it obviates any gas cutting that is possible from a thread alone.

"In the case of a real mono-block, as the name implies, a mono-block is one solid piece of steel, milled from a known aloy. With this one may fit the block to the action and rough finish to shape befor barrels are even aquired. There is no solder involved at this point. the barrels may be turned to fit two holes through the mono-block, and can be fixed there by threading, and press fit, or silvering,the barrel shanks, and fluxing, the mono-block, heated, and barrels pressed into place, and cooled. At this point the stress relief can be done any way the maker chooses. I personally whould go the Cryno method with any of the systems involved posted on this thread. The true mono-block can be tigged, with little problem in relieving stress by the method you choose.
"

In this process there is no need for stress relief as there are none set up unless the barrel joint is welded.

In respect of Cryo stress relief generally, this is not suitible for welded CrM steel as the steel needs to be heated to its normalisation tempreture to realign the crystaline structure, rehardened and tempered. Cryo will not and is not, designed to achieve this.

Regards