I'm not a big past champion's provisional fan (I don't think anyone really is).
If you're going to do a gimmick, just come out and do a gimmick. Have a promoter's option where Eddie Gossage bursts fireworks into the sky forming the likeness of whichever driver he wants in the show for all to see, declares it fate, and puts that driver in 43rd. Or have a fan vote...the fans were used to determine the fastest pit crew at one point, surely we can determine the fastest 43 qualifiers.
But seriously, the only way to get rid of the PCP is to make sure Jeremy Mayfield never gets back in the garage looking for scrap metal...
The only way to get rid of the other kind of PCP is to have it do something really awful. First race of the Chase. 44 cars entered. The 8 slowest are the top 7 in owner's points, who are also the top 7 in driver's points, and ol' Texas Terry Labonte on his #32 Hoveround. 7th place just so happens to be named Earnhardt. The provisionals page of the rulebook magically gets blacked out and Terry "decides" to retire immediately.
By the way, I'm looking forward to Danica in a GoDaddy.com Toyota for Humphrey-Smith after her first DNQ. I say this as a Danica fan, but even more as a fan of amusing things, and I really want Lionel to be pressured into making 36 varieties of Danica die-cast to commemorate each different ride she bought in 2013.
Knowing NASCAR, and Danica, though, I suspect a new declaration will allow Tony Stewart to use the 2011 champion's provisional for himself and loan the 2005 and 2002 ones to Danica and Ryan respectively.