Is the shifter button an issue on the SHO like it is for the Explorer? Occasionally, I get a message in the message center when I shut off the car that says "shift to park". Flicking the shifter button a few times trips the switch and allows the vehicle to realize it actually is in park, and the message goes away. I've never tried starting in this condition, but I imagine it would not allow it.
Next time you experience the issue, confirm the "P" on your gear indicator is illuminated orange (or red - I'm color deficient). If everything is white, then it doesn't know what gear it's in, and flicking the shift button until the "P" lights up orange/red should resolve it.
Not sure if this is your issue, but something to keep an eye on, since moving the shifter seemed to have a temporary positive effect.
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