As a runner, I've had PF several times (I actually feel another bout of it coming on). First time I saw the doc about it he explained the morning pain to me this way: During the night, your foot is in a relaxed plantarflexion position (see attached pic). And all the heeling that happens is pulled out when you first get out of bed, take steps, and the foot goes into a neutral and dorsiflexion position. So, as others have indicated...the boot is the way to go so that the heeling that happens while you sleep happens in the the dorsiflexion and isn't pulled out when you take steps.
Granted...sleeping with the boot isn't exactly comfortable (and the sock is worse). But it usually only takes a few nights. Good luck.
Dan