The rim of the 5.45x39mm is .393",chamber pressure ?but the 222 Remington has a 50,000psi max chamber pressure launching a 52 grain bullet at 3100fps. Which is what the military load does in the 5.45x39mm(54 grain bullet at 3084.14fps).
The rim on the 6mmPPC is .443" and the chamber pressure is 60,000psi.
The rim on the 7.62x39mm is .443" and the chamber max chamber pressure is 45,000psi.
The rim on the 6mm Remington is .473" and max chamber pressure is 65,000psi. The empty 6mm Remington case is .003" longer than a loaded 5.45x39mm or 7.62x39mm round.
The rim on the 223 Remington is .378" and max chamber pressure is 55,000psi.
So as you can see the 6mmPPC cartridge would have to be downloaded but is the only one that would not require lathe work on the bolt face of a 7.62x39mm rifle. The downloding would work out fine as the less powder the more room to seat heavier bullets and still fit them in the magazine.
While a cheap take off barrel sounds good the lathe work is going to cost some bucks as besides chambering the AK barrel has 6 steps in it. So the barrel will have to be turned to 6 different diameters.
www.k-var.com/product.asp?0=216&1=219&3=143