How to install if wall is too deep for wall AC unit

this may be an issue, you need to verify the air flow patterns over the condenser coil. If there are louvers in the sides that would be the "intake" for the coil and it will definitely not work if these are blocked. You may need to make the opening larger and mount the sleeve from outside as it would be better to have the controls closer to the outside wall than the air flow blocked by the wall.