Possibly the solution is with a caliber adapter for a standard 7.62x39mm type AK. Rimfire adapters exist for the M-16/M-4 originally for use on indoor ranges.
It seems that a conversion bolt, a barrel/chamber liner, and an adapter magezine may solve the problem. The .22 cal bolt would have no locking lugs and allow elementary blowback operation. The cartridge ejector could be the corner of the mag as in the German Voere .22's and some others.
If cycle energy proves too low a lighter "k" recoil spring may solve it. If more cycle energy is required perhaps a special chamber insert such as Carbine Williams developed for the .22 cal 1919 BMG conversion. His chamber adapter-insert acted as an internal drive piston.
Some thoughts for fellows with well-equipped shops.