You don't seem to be listening. Installing a large, left-in-place plate is a bad idea. You will essentially be underpinning a variable thickness of soil below the bottom of the stone foundation wall.
Your sketch does not show any lateral support for the underpinning. Don't forget to check the underpinning for overturning and sliding.
Here are some photos for some rubble stone walls.
Try sticking a steel plate under this rubble stone foundation wall.
Note how the bottom of the rubble stone wall can vary. Where will you place the plate?