Not sure I can do anything about this.....

Since it's just an electronic switch rather than a mechanical lever, I would bet money pushing P when the vehicle is moving doesn't do anything. But, I'll let someone else be the guinea pig.

 

It does nothing (or maybe switches to Neutral), above a threshold speed, 7 mph maybe. Below that threshold you come to an abrupt stop.

 

Yes, above a certain speed it beeps and switches to neutral if you hit "P". I already tried that, accidentally, at about 50 mph. To make sure that doesn't happen again below the critical speed, I put an easily lifted hinged cover over the button. No, it's not pretty, but it works.

 

Thanks for being Guinea pig!!
Good to know.
Your solution seems in the same vein as the covered and protected ejection seat switches in military aircraft. If the computer did not safety-override a P press at higher speeds, I would certainly copy your approach as the results of actually engaging the parking gear pawl at high speeds is extremely destructive and potentially hard to control the results, just as an ejection means losing the aircraft, compressing your spine by about an inch, and encountering unknown hazards on the way down.
I also care about function more than pretty, although having both is nice.