Here's what I would consider - buy a $20 Suomi kit and a few mags from CFS. Other mags can be dug up elsewhere, but the Suomi stuff is pretty cheap right now.
Take the barrel out of the Suomi and discard (or sell) the rest of the kit. Now you've got a barrel blank that you can thin down on a lathe, put on a barrel extension, and you're good!
Suomi mags will need to have a locking lug welded on, or you could make a "magazine well" to engage them in the receiver. Either way, the mags won't simply lock up without a bit 'o' work. It would be best to use a magazine well so you only have to touch 1 part instead of welding on 10-20 magazines.
Mags, I would also look PPSH mags. I think they will work with some refitting...
PPSH barrels can be had for about $40 but they too require a barrel extension.
I've looked for carbine-length 9mm barrel blanks and can't find any. I can find .358 barrels but none listed as "true" 9mm barrels.
Here's a thought - I haven't pursued this - the Uzi guy that makes barrel conversions for the Uzi may be able to make something. It would require sleeves to fit, but would be the proper length. If I remember correctly, it is firstname.lastname@example.org - let me confirm... yep it is. He can be found on uzitalk.com as well...