You're stuck.
Sadly, it's hightly likely that those P1's will go.
And even if they don't sell outright, then here's what happens.
Cunard upgrade some people from (say) B/C1 to P3.
The P3's go to P2
The P2's go to P1
The P1's go to Q3
etc etc etc
That way they clear space in the lower priced cabins which they then offer as 'super saver' last minute deals.
So - you *could* be lucky to be upgraded - but you can't rely on it.
I can't think of a way that you can bump up without paying the full whack.
Cunard is in business to make money and they'll not be easy to beat down on price unless you can offer them something that makes it worth their while.
For repeat customers it's easier.
Maybe you could play a waiting game and keep ringing them every day. If the Px cabins are not selling, then you can offer to make a deal whereby you'll take it at a certain price.
To them, a guaranteed sale *might* be more attractive because what you're doing is pre-empting their 'work' ie. You're upgrading yourself (and paying for it) which they might have to do anyway without getting any more money for it. This'll only work if there are free cabins somwhere up the chain. ie. They can make a P1 free by bumping the current occupants up to a Q3, freeing it for you.
Beware though - Cunard (as all cruise lines) are very coy about how they do things and they are EXPERT at judging what's possible. They'll not let on to you what position they're in.
They start their 'upgrade' process about 1 month before sailing date, sometimes these changes are taking place 2 weeks before departure. You can tell that something might be up if you don't get your tickets 2 weeks before departure. When your ticket comes up for printing the system checks to see if there are going to be any last minute changes needed. If not then print and send, but if your cabin is needed (ie. that cat is full) then it'll look up the line to see if there is free capacity and then it goes to customer services who do the calling around to 'reshuffle' the cabins. Beleive it or not, some people do not take the offer of an upgrade. Some people like to stay in Px cat because they particularly like the Princess (and/or Britannia on QE2) Grill restaurants.
Best of luck anyway.
P