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I don't have my Model S anymore but when I did, I measured the length from the rear central A/C vents and it was about 76" which could easily accommodate one side of your 4x4' plywood.
However, the trunk's width was only about 39" so you cannot lay your 4x4' plywood down flat.
I imagine you can tilt your 4x4' plywood to fit it in the Model S.
On the diagonal (front to back as well as side to side), it can barely fit. To be safe, I prefer putting it vertically behind the back seats better, because I don't want to mess up my upholstery.
Don't EVER try to put a bale of alfalfa in the back of a Model S. You can jam it in there, but you'll have to take it out piece by piece. It's a nightmare, I speak from personal experience. Took 2 months to remove all the alfalfa bits.
^this. I just measured and 45" is about max on the diagonal, and you would certainly be scraping your car in some way. I don't understand how anyone could get it in from the side in the back seat. The rear doors have about 35" of clearance in height, and just over 40" diagonally. You are not getting a 48-in square piece of plywood in according to the measurements I just took in my 2017 Model S.