I happened to have a .38 Special round on the desk, and just for kicks, stuck it to a Maadi bolt I had on hand. The extractor gripped the rim just fine. The .38 rim diameter was within .001" of the 7.62x39 cartridge I checked, as was the thickness.
Isn't that *interesting*...
I found Desert Eagle .357 magazines for $45 online. An AK in .357 Magnum would be nifty if the magazines weren't so expensive.
If I could still buy a kit in a bag for $75 I'd be tempted anyway.