Couple of points to consider...BA to MAN is in T1 and AA to BOS will be from T3 so make sure courier is delivering PP to wherever you plan to be.
On occasion I have pre-checked people in to Scandinavia who were having PPs delivered late...but never with a connex to the US and I doubt BA would be so kind anyway.
I would hazard a guess that you should have $200 spare in your pocket...