OK, I just wanted to establish a "visual" in my own head, but can't actually help except to suggest Numrich Arms.
I scanned a little bit quickly (not very thoroughly) through their website for those brands looking for s20 and s41 but didn't see anything. Might be worthwhile writing to them, though, with a picture of both the barrel alone and the assembled gun. They may gave something tucked away somewhere that they didn't know right away what it was (unlikely, but possible.)
My son and I spent a couple of years browsing around looking for a replacement barrel for a particular nickeled S&W handgun and finally found one and restored the gun to serviceability.
If you're really stuck and married to the idea of shooting .22 from your gun, there are inserts available which allow firing .22s from a shotgun barrel. I understand the accuracy of these is not great, some are rifled, some not, and there's a problem of not having rifle sights on the shotgun barrel, etc, etc. Some require insert plugs to convert the centerfire to rimfire, and some have the .22 chamber offset in the insert to work as a rimfire without conversion plugs.
This is only a sample of what's available --I don't know if these inserts go all the way down to your .410 gauge, but I'm just trying to be helpful:
I don't have any idea how Hawaii's registration laws work with chamber insert devices, or if they're considered pistols, or anything else. Like I said, just trying to be helpful.
I'm still curious about what happened to the .22 barrel. Did it just not come with the gun, or do you actually have it and it got ruined somehow? Or lose it, or what?
Terry