Converting the Sten mag could be easier than you think: Mill out the depression in the back, weld a new "back plate" on the entire mag, with the appropriate cut out for the latch in the Sten or the SOCOM block. It still works in the Sten, and now can hold the longer rounds.
Considering there has been at least one UZI in 7.62x25 ... I checked that mag, the only way that conversion worked was by using a round with shorted COL (using the HP/XTP bullet).
Another option are the official 7.62x25 mags and making a mag block for those. They will hold the 9x23 without a problem.
Last but not least, the m-1 carbine magazine will hold these rounds with room to spare. The carbine has been offered in 9mm Win Mag, so the AR could work as well. For the 50AE, a spacer is installed in the standard AR mag and a new follower made. Why not something similar for the 9mm Win Mag?
Just some idle thoughts
M