I have been wanting them to make the Handi in auto pistol calibers too. I think it would be good for plinking and some small critter work. No doubt 9mm is the most common pistol round on the planet, and I can see the desirability of a good foraging gun in a scavangable round should things go that way. While we're at it, how about .40 and .45
We have a couple of options to get what we want, and I would put firing 9mm through a .357 Handi toward the bottom of that list, even if you do have duct tape.
First option is making or having made a new barrel by 'stubbing' an existing barrel. This has been a topic here recently and I think that stubbing a Handi will be one of my next gunsmithing projects, after the projects on my bench get further along. In short, you put a barrel blank into the cut off stub of an existing barrel and re chamber to the new cartridge. (Now is where you get to use that 223 extractor.) On the good side, you end up with a high quality barrel. On the bad side, if you can't do it yourself you will spend more than the price of a new handi to get it done. At that point you could have just stocked up on ammo for the .357. Check out the FAQ section. I did and it got me hooked. There shall be stubbing here.
Another option is buying a barrel insert. I know that MCA in Alaska sells full barrel length inserts that slip into a 12g barrel to fire smaller rounds. (same outfit that sells the chamber adapters) I haven't got any response from them to any of my emails, so I don't know how easy they are to deal with. That may be a good option because you could have a couple of inserts that you could choose between as ammo became available. You would also have the 12g barrel which is not a bad foraging round at all. I would guess that the humble 12 gage shotgun accounts for as much game in this country every year as any two other cartridges together.
At the moment, I have a 9mm carbine project that I am wrapping up. I took a Spanish Destroyer carbine ( bolt action carbine originally chambered in 9x23mm) and shortened the chamber. Not too difficult. I took the barrel out, cut the barrel shoulder and breach face back enough to turn it two more turns back into the receiver. Now the sights will be where they should be and I will only have to ream the chamber a few thousandths by hand. I will be fitting modified 9mm 1911 magazines to feed it. The machining is done, just time to reassemble, swear at whatever I'm overlooking, and straighten it all out.
You are on a good track. The Handi rifle is a great platform for experimentation. Build something that you want and can't get off the shelf. That way, if the SHTF, you have the gun. Even better, if the S never hits the fan, you will have learned something and done constructive things with your time.