I really don't think he would. Considering that all libel trials have to take place in the High Court, how lengthy the build up is and how generally the bad publicity generated from full reporting on libel trials often leads to more public damage than the initial accusation/wrong statement, I very much doubt that the Queen whose very effective motto has been "never complain, never explain" would countenance paying his legal bills for that.
Can you imagine mumsnet calling witnesses to explain why, in common parlance, the meaning of "peadophile" has changed to include a widely accepted colloquial meaning beyond its strict academic definition, and then the RF trying to explain why they are seeking to close down free speech amongst their subjects so as to financially benefit a man who has already paid out millions in civil damages for something he allegedly didn't do?
The best way forward for PA now is to quietly enjoy his wealth and privilege and to keep his head down, not seek out more notoriety. Libel trials often spectacularly backfire, even when they don't include matters that people are notoriously touchy about such as exploiting very young vulnerable teenagers.
Then you have to consider how many times online the same allegation has been made and how the RF and PA would justify coming after a bunch of mainly women...absolute PR disaster.
Then, in order to win damages, PS would have to prove that he had lost work or commercial income due to the damage to his reputation and not due to his own conduct. That too, would have to be fully explained in detail in evidence, including evidence relating to commercial enterprises that those involved would undoubtedly prefer to remain secret.