If you're attempting a higher degree of accuracy with a rifled insert, the method used by some European combination/drilling gunmakers is an insert with a threaded muzzle nut. In German, they are called Einstecklaufs, and Krieghoff's are probably the best known. Most are also designed to work with the existing extractor systems, so you won't need a rod to poke out empties.
Ammo holder/wallet for drillings & combination guns. Holds up to 9,3x74 & 12 ga. Small elastic loops for your einstecklauf (sub caliber insert barrel) ammo. Classic German hunting stag (St....
classicsportingguns.com
Downside? Crazy expensive, like $500-1K.
Here's a link to one company's offerings:
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At one point Tanfoglio made a broadly-similar type of insert with an external muzzle nut, marketed in the USA via EAA in 45-70-to-12 ga. I don't see it currently listed at the EAA parts website.
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Here's a link to the manual from EAA:
Manual for the 45-70 Conversion Kit by Tanfoglio
issuu.com
The protruding muzzle nut is perhaps a bit inelegant-looking, but the thing I like about it is that it positively positions the rifled insert under tension in the same manner as the interchangeable barrels on Dan Wesson revolvers.
I suppose one of the longer Chaszel insert barrels could be threaded and fitted with a similar external muzzle nut to mate with a shorter shotgun barrel in a manner similar to this, though you'd also need to cut a relief notch at the breech end for the extractor.
I own a single-shot Erma .22 LR adapter for the 7.92x57 K98k service rifle. It will also fit into just about any other bolt action in the same chambering and barrel length -- it works on my Husqvarna sporting rifle equally well. This adapter barrel uses an external muzzle nut similar to the Tanfoglio/EAA example. The muzzle nut is tapered at the rear and centers the insert as it tightens down and seats against the muzzle crown.
I can confirm that it has been very accurate at the short indoor distances I've shot it so far (unfortunately the target shown in this short video includes some sighters from zeroing the scope.)
This is an expansion and re-edit of my earlier video, with audio and shooting appended. (text continues below)Granted, most of the audio is the sound of noi...
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BTW, I've not read every reply in this thread, so forgive me if this sort of insert system has been discussed previously here.