I have a 3/4" aluminum "board" across the inside of my transom, with a 3/4 wood board over it on the inside. And then I believe 1" thick wood on the outside transom. Plus the thin sheet of aluminum. So that's a total thickness of about 2 1/2 inches that I'm using with my Suzuki motor. And as Locomotion says, the clamps of my motor would not fit over all that wood. (But your Johnson clamps may allow thicker than my Suzuki.)
So what I did (60% by design and 40% by hindsight) was recess a couple of holes for the clamp pads into my inner wood, which probably reduces the total thickness to about 2 1/4". This means I cannot remove the motor without unbolting and removing that inner wooden plank with the motor. I.e., when I unscrew my motor clamps fully, the clamp pads are still trapped in those recesses. I chose to do it this way after seeing someone's motor jump off the transom when their steering cable broke, and being warned by a few of the guys to check my motor clamps everytime I put the boat in the water. I'm not sure what would be better: to have the motor jump off the boat when the motor kicks over to the side, or to have it remain attached. Hopefully I'll never find out!
Here's a picture showing V1 of the wood on my transom, with the clamp recesses. I'm now on V2, because that fiberglass over plywood didn't hold up very well.
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You can go up to what ever the clamps will fit over, I have run a 3/4” thick inside with a 2” outside board with good results.
The thicker outside board puts the prop deeper as the engine is moved further back and down as the result of the angle of the transom, which is usually about 14 degrees.