First of all, the CPS can review a case at any stage, right up to the courtroom door on the day of the trial, when they'll have a barrister there. I have known the CPS persuaded, by their barrister, that their case is not winnable ,even at that late stage, and so no evidence was offered (i.e.the defendant pleaded not guilty and their counsel said "I offer no evidence on behalf of the Crown" and a not guilty verdict was entered).
This fourteen day rule you found on the CPS site is because the hearing at the magistrates' court, from which you are sent to Crown Court, is a mere formality, often with papers served at the last minute. Formerly, this was less so and witnesses were called to give evidence, or their statements read, to show whether or not there was a case to answer, witnesses were questioned or points of law raised; you could call the defendant to give evidence. Those days went . Nearly every case was a 'paper committal for trial' and very rarely did anyone try to stop the case then and there. So this provision serves the old purpose; if you can disclose facts and arguments, having had time to consider, to show that the prosecution is ill-founded, the CPS may give up, and safe public money.
This provision itself not going to help you because, by the time you have expert evidence, the time will be up ! But that is only a convenient provision, it doesn't alter the basic rule as set out in my first paragraph. And anyway, apart from the alleged confession, the CPS have the woman. Unless she is obviously not to be believed , as much a judgment of officers who have seen her as of the CPS, the CPS will go on. There would be so much flak caused if the prosecution did not go on to charge and have tried cases when a woman complains; quite right too, because it makes no sense to treat a woman differently from a man or to require that her evidence be independently supported; and so they will.
But, as in all trials, the prosecution version is only one side of the story. I'd say that about half of contested trials result in acquittal, so juries do not demonstrate the utmost confidence in the prosecution case !
For now, leave it your solicitor and barrister, in due course, to find any expert evidence that may be required and prepare to attack, in any case, the other side's evidence by establishing consent or the reasonable possibility of it.