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You are grossly over generalizing about what 5psi higher will do. 5psi is not going to cause those issues. Going to have to get more carried away adding pressure than that to cause those issues.
The stock pressure is what they feel was the best all round compromise for a lot of factors, 5psi is going to shift the balance they chose, not stop the tire from functioning. Would probably hurt snow grip, but reduce what little sidewall roll there is cornering. 5000lbs cornering hard is going to roll the tire more than you expect.
The late 2014, early 2015 P85Ds had a sportier set of suspension dampers. You could, in theory get a set of those, but I'm sure those would be touh to come by.
If your car has more body roll than in the video something is wrong. Have someone take a video of you taking a hard corner after putting the car on low suspension (set the speed limit to always then take the car up to 50 MPH to be sure). Either your perception is off or you need a trip to the SC. The ride height may be out of calibration.
So I tried your +5 psi but that was definitely too much. I'm now running at 45 psi and it has stopped 75% of the body roll I was experiencing. I guess the weight just put more pressure on the tires.