OK I think I just figured something out! I think you can use a FAL FCG for this, or something very similar. It would just need to be "thin" enough to fit in the empty space on the side.
Here is my idea:
Lay the hammer and disconnector on their RH side, LH side facing up.
Modify both the disconnector and the trigger to add a 45 degree slope on their adjoining lip. The trigger may need a slightly taller back-end, which may need to be farther to the side.
The action is identical to a normal FAL action. The difference it that both the disconnector and hammer axis is vertical, and the sloped face of the trigger pushes upward, forcing the disconnector to move left-right on its vertical axis.
The trigger frame could contain the ends of the axis pins, the tops of which could be set into holes in that blocking shim.
Modify the shape of the hammer to fit.
For the spur that prevents out-of-battery misfires, a block could be placed on the carrier in that area in-between the top of the recoil spring and the bottom of the bolt. There is a threaded hole there. That hole could be the mount point for the spur. The spur would be oriented like the AK's in such a way that the hammer cannot touch the firing pin until the bolt is in battery.
I'm sure that would work!
Are you saying a totally new grip housing and throw away the old? I don't think I would need a new grip housing. What I would do is yank the guts out of the existing housing and replace with the FAL trigger .