It's been done before, but it's really not practical from a cost standpoint given you can buy a brand new H&R Handi-Rifle in either caliber mentioned for under $300. Another (and nicer) option would be to find one of the older Savage Model 24V's in .357 Mag/20ga, but that would be more money yet ($600-700 typically as they weren't nearly as popular as the 22's).
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