I found this post on making rimless 444 Marlin using 6mm Remington brass. I didn’t chech the casehead sizing. But it might mach up well enough with the 762×39 to work.
I can’t see how a .243 can go up to a 44 if a 308 can’t but it’s not my project. But it does make me think cutting the top off a 30.06 to make 444 rimmless brass could posibly work. I’m telling you right up front I haven’t checked any case dimensions. But it is an interesting idea, an AK thumper in 444 would be a cool gun.