Please help me with this issue.

Current assembly
I feel I need to stiffen the walls more than the current plan accomplished. Tile will be on one side. I actually don't need to stiffen the other side but these drawings indicate that intension. So There will be tile on the wall that is oriented to the bottom. The walls are 6". They have 2x4 set on the sides with the notched out areas to recieve the 3/4" ply that is inlayed and screwed in place. There is still some flextion. I do not want to t take out the wall at the point. I have been wondering if the 2 methods I've shown below might be helpful. My carpenter thinks that with the CBU it will stiffen it up as is.

Option 1a -
Using wood glue and screws every 4" oc, set in 3/4" plywood on the interior side of the assembly. New ply is shown in green. I would do this by taking off the black panels shown at the top of the illustrated assembly "NORTH", while "SOUTH" panels are still in place. I would roll the glue on and stand up the new ply panels and scew in place. All while the re-enforced wall is in place, standing. I don't need to re-enforce the north panels as the wall is fairly stiff as it is for standard drywall application and usage. 1b - Take off the "NORTH" panels, mark the "SOUTH" panel placement within the stud space. Next remove the "SOUTH" panels and glue up, dry, and replace.

Option 2
Idea to put angle iron, full length, at the stud and ply intersection as shown in red. These would be either epoxy in place, screwed in place, or both.

If there are better ideas let me know. Thanks for taking the time to consider this issue.

Current Pocket Door Assembly- Plan View