Clever idea to use a subcaliber adapter as a chamber insert.
Worth repeating:
The .22 barrel face must be brought back to the bolt face. There must be just enough gap between the bolt and barrel to allow the bolt to close.
Keep headspace to a minimum. You don't want the case head to bulge.
Only cut the extractor notch as much as necessary to allow the extractor to grip the casing. Otherwise, the case will bulge.

I use slow curing epoxy to bond the chamber insert and liner in place. There isn't a whole lot of force trying to push out the liner, and there is lots of surface area for the bond. I've successfully used epoxy to bond in a 9mm liner.
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